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Kodegadulo 
Posted: Jun 23 2012, 09:12 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
EDIT: This system has evolved over the years. See the Primel Metrology Wiki for the most uptodate description.
The Primel Metrologyor: What if we start with the hexciaday?Note: This post has been revised based on possibilities explored in later discussions in this thread. But you can find a snapshot of a previous version of this post here.This thread will serve as a reboot of my investigation into the potential of the "Primel" metrology. The goal of this effort is to see whether a viable system of measurement can be constructed using many of the same principles that Tom Pendlebury embodied in his TGM metrology, but starting with a somewhat different set of initial conditions. The chief principles I want to preserve in Primel are: (1) 1:1 correspondence between related physical quantities and the eschewing of extraneous scale factors; and (2) basing the system on fundamental realities of common human experience of life on Earth, including the mean solar day, acceleration due to Earth's gravity, the density of water, and so forth, but not necessarily including (nor necessarily precluding) universal constants such as the speed of light or the fine structure constant. The chief point of divergence from TGM is to start with a smaller base unit of time, namely the hexciaday (h↓Dy), which is 10^{6}_{z} days, rather than TGM's pentciasemiday (p↓2\Dy) which is 6×10^{6}_{z} days long. This was initially motivated, in part, by the perception that some of TGM's units are "too large", particularly the Volm, the unit of volume, and the Maz, the unit of mass. However, I believe that issue can be mitigated somewhat by using a combination of multiplier and power prefixes from Systematic Dozenal Nomenclature to identify "humansized" scalings of the base units, and then coining colloquial names for those as auxiliary units (e.g. Pendlebury's "tumblol" for the trinabiciaVolm (t•b↓Vm), a close approximation of the U.S. or Imperial pint, and the "pounz" for the trinabiciaMaz (t•b↓Mz), a close approximation of the Avoirdupois pound). We are likely to find this technique useful to mitigate perceived problems with the sizings in the Primel metrology as well. So rather than viewing Primel as a "cure" for problems in TGM, I'd like to approach this as an exercise in vindicating the basic principles of TGM, and a chance to get some fresh insights into how rational systems of measurement can be constructed. First, a couple of conventions: To name its base units, Primel will make use of Quantitels, "anonymous" names for units derived (relatively) directly from the terms for the quantities they measure, by appending a common "el" ending, standing for "element of", by analogy with a "pixel" being an "element of" a picture or image. "Primel" serves as not only a label for the entire metrology, but also as the disambiguating adjective which can be prefixed onto Quantitels to distinguish Primel units from other systems that also use Quantitel nomenclature, as well as from the use of Quantitels to speak generically about units of measure. However, rather than repeating this adjective ubiquitously, Primel Quantitels will be prefixed with a prime character ( ′ ), which can either be pronounced "Primel", "prime", or not at all, whichever proves most convenient depending on the circumstances.
As of 11EE/09/1E_{z}, I've revised this post to follow the convention spelled out in The Duodecimal Bulletin, Volume 52_{z}, Number 1, Whole Number X2_{z}, in the article "Base Annotation Schemes": Every dozenal number will be annotated with a subscript "z", every decimal number with a subscript "d", e.g. 100_{z} = 144_{d}. The rest of this post will serve as an executive summary of the results of this investigation, so it will be edited from time to time to add results as they are accrued; but such changes will be announced in followup posts. Primel Base UnitsThe following table lists all the base units of the Primel system derived to date. This just lists the base unit for each physical quantity, for reference and definition purposes, without considering scalings and colloquialisms. See later subsections of this post (TBD) for more detailed treatments of each physical quantity tailored to the most convenient humansized usages. Subscripts indicate base: d = decimal, z = dozenal. Greyedout digits are provided for completeness but were computed and should be taken with a grain of salt.
Note 1: The ′temperaturel is approximately the change in temperature induced in 1 ′massel of water when 1 ′workel of heat is applied to it. The canonical value is rounded up so that a whole number (250_{d} = 18X_{z}) of ′quadquatemperaturels fit between the freezing and boiling points of water under standard atmospheric pressure. Note 2: The ′currentel is the amount of current flowing through a pair of wires one ′lengthel apart, sufficient to produce a magnetic force between them of one ′pentciaforcel per ′lengthel of wire (defining Ampere's magnetic force constant as k_{A} = 0.6×10^{5}_{z} ′Wkℓ/′Crℓ^{2}). Note: Even as late as 11EE/09/1E_{z}, the whole electromagnetic subsystem is very much up in the air. The above reflects an earlier approach based on Ampere's Law, following a pattern similar to what Pendlebury did for TGM. But I am also considering an approach suggested by Gingerbill, jrus, Wendy Krieger, and others where the ′resistel is set to the vacuum impedance. See Primel Metrology Wiki Note 3: The ′substancel is an amount of a given substance with the same number of particles as there are in 10_{z} ′massels of pure Carbon isotope 10_{z}. (The name of each physical quantity above will (eventually) be a link to a followup post which goes into detail about its associated Primel units.) 

Treisaran 
Posted: Jun 24 2012, 11:59 AM


Dozens Disciple Group: Members Posts: 1,221 Member No.: 630 Joined: 14February 12 
I don't think this is a problem when used as a radix point, only when used as a base marker akin to your former use of a subscript after the number. I've seen hideous examples of two consecutive semicolons, the one being a base marker and the other a punctuation semicolon, but the Humphrey point when used inside numbers as a separator between the integer and the fractional part doesn't suffer from this problem. Note also that the punctuation semicolon is followed by a space, while the semicolon as radix point isn't.
I concur, though I'd actually prefer × (U+00D7) as a multiplication symbol but for the fact that there are not one but two Xlike symbols to clash with: not just the algebraic x (I remember switching to · once I started prehigh school algebra) but also the X a lot of us, including me, use for ten out of necessity.
Again, I think this isn't an actual problem. The punctuation full stop, like the semicolon and the comma (which latter the Continental Europeans use as a decimal 'point'), is followed by a space, while the radix separator isn't. It's a far cry from the use of punctuation marks in names, like 'Yahoo!', in the middle of a sentence which is really in conflict with punctuation usage. Even my use of an asterisk for marking dozenal numbers, though it could be improved upon, doesn't conflict with the punctuation asterisk, because it comes before the number while the punctuation asterisk comes after the text. One good sign of a true clash between usages is that it's blatant, it sticks out, it becomes one of the pet peeves people talk about at the pub. 

Kodegadulo 
Posted: Jun 24 2012, 02:14 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Let's redirect this sidediscussion to here. 

Kodegadulo 
Posted: Jun 24 2012, 07:52 PM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Edits to the original post:

Kodegadulo 
Posted: Jun 25 2012, 05:39 PM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Edits to original post:

Kodegadulo 
Posted: Jun 26 2012, 09:44 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Time UnitsNote: If you read this post, realize that it's obsolete. I've supplanted it with this later post, where I've changed the colloquialisms for the units. I'm keeping this one around for historical reasons to avoid confusion, rather than editing it.The mean solar day is a fundamental reality of Primel, just as it is for TGM. However, Primel will use a round dozenal power of the day, the hexciaday, as its base unit of time, the ′timel. This contrasts with TGM, which first divides the day in half, and then takes the pentcia of the semiday as its base time unit, the Tim. As a consquence, the ′timel is equivalent to onesixth of a Tim. This makes the ′timel a very fleeting moment of time, just beyond human perception. (I have proposed calling it, colloquially, a "′twinkling".) Nevertheless, it is a useful quantity for precision scientific and engineering purposes, and its scale will have interesting effects on the rest of the Primel metrology. On the other hand, the unqual powers of the ′timel, starting with the unqua′timel, do fall within the human scale. The table below shows a range of dozenal powers of the ′timel, from ennqua down to enncia. The ′timel itself is highlighted in blue, and the "human scale" powers up to the full day are shown in green. Each of these is equivalent to an uncial power of the day, and these equivalents can be used as synonyms. One useful feature to note at the top of the scale is that higher powers of the ′timel correspond to whole powers of the day, so there is a seamless transition from largescale measures of time based on the day and smallerscale measures of time.
The unqua′timel is equal to 2 Tims or about a third of a second. It is equivalent to a beat of a metronome in the presto range. Counting unqua′timels in threes approximates the tempo of a Viennese waltz. A gross of unqua′timels constitutes a triqua′timel. The triqua′timel is noteworthy in that it is also the triciaday, making it exactly intermediary between the ′timel and the day on the exponential scale. Calling it a "′trice" therefore makes for a nice play on words. Alternatively, at d50 seconds it is very close to a conventional minute, so giving it the colloquial name "′minute" would be quite reasonable. A dozen (z10) ′minutes is equivalent to ten (d10) conventional minutes, which might be called a "′segment". A gross (z100) ′minutes is equivalent to a long hundred (d120) conventional minutes, which is the same as 2 hours, an uncia of a day. Using an SDN prefix, we might call this a "bihour", but perhaps a less derivative expression would relate it to the fact that it is about the duration of a typical sitdown entertainment performance, such as a featurelength motion picture, or a musical concert, or a theatrical play. Although the TGM time units are not whole dozenal powers of the ′timel, they are all a simple multiple of one, so we could certainly incorporate them into Primel as auxiliary units:
Here are a few additional auxiliary units that are all interesting multiples of some dozenal power of the ′timel:
(A Perennial Calendar can be constructed where every year and month starts on the same day of the week, where every year and month contains a whole number of weeks, and where a leap year adds a leap week onto the last month of the year, rather than a leap day in February. The pattern of leap years would be quite different, of course. When such a calendar is interpreted in dozenal, there's a nice sort of correspondence between how each month is either z24 or z2E days and how each year is either z264 or z26E days; or equivalently, how each month is either 4 or 5 weeks and how each year is either z44 or z45 weeks.) z[


Kodegadulo 
Posted: Jun 27 2012, 02:36 AM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Acceleration/Gravity UnitsThe acceleration due to the gravity of the Earth is the next reality of the Primel system, as it is for TGM. Primel standardizes its ′accelerel (identical with its ′gravitel) on the SI value for \(g_0\), the normal or standard gravity. SI specifies this value as exactly d9.80665 meters/second^{2}. This makes it very precise by definition without requiring precision of measurement, and it is, by definition, within the range of acceptable values for Earth's gravity. So I don't feel there is any need to look for some other basis for defining a gravity value, such as the polar diameter of Earth. Being able to relate the Primel ′gravitel directly to SI's gravitel would seem advantageous. However, this means the Primel ′gravitel is only a close approximation for the TGM gravitel (the Gee), and consequently all other Primel units derived from it will be only approximations to the corresponding amounts of TGM units. Table 1 lists the gravities expected at various latitudes, as calculated using this formula. The attached image shows a plot of these values. Tables 2 and 3 list actual measured gravities at various major cities around the world. Table 2 lists the cities in alphabetical order. Table 3 sorts them from lowest to hightest surface gravity. Table 4 shows a comparison of the surface gravities for the various bodies in the solar system.
Additional material: There are interesting discussions about gravity, and the ′gravitel, in these threads.


Kodegadulo 
Posted: Jun 27 2012, 04:11 AM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Velocity/Speed UnitsThe Primel base unit for velocity or speed, the ′velocitel or ′speedel, is derived by taking the product of the ′accelerel and the ′timel. This represents the amount of speed a falling object picks up in the first jiff (z42 triciaseconds) of its descent. Remarkably, this yields a speed that is very close to one customary foot per second, and very close indeed to one kilometer per hour! The table below shows the unqual powers of the ′velocitel, up to and including the Einsteinian limit \(c_0\), the speed of light.
Here's a comparison of the kind of speeds you'd find on an automobile's speedometer dial. Although as dozenalists we'd prefer to use dozenal numbers with Primel units, I present the decimal values along with the dozenal values, in order to highlight the close correspondence between speeds expressed in ′speedels and speeds expressed in KPH
There's also a nice correspondence between z20 ′Veℓ and approximately d15 mph. You often see speed limit signs in the U.S. in increments of d15 mph d15 mph, d30 mph, d45 mph. Note that z70 ′Veℓ is very close to d55 mph which is common as the metropolitan highway limit. d65 mph is common as the crosscountry highway limit, and d80 ′Veℓ approaches it, though not very well; however some states, especially rural ones, have reinstated d70 mph as a limit, and z90 ′Veℓ approximates that very closely. 

Kodegadulo 
Posted: Jun 27 2012, 09:07 PM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Added a depiction of a Perennial Calendar in the post about Time Units.

Kodegadulo 
Posted: Jun 30 2012, 06:46 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
CAVEAT: This post reflects an earlier point in the evolution of Primel, when I was using the SI gravity of 9.80665_{z} m/s^{2} rather than the gravity which achieves ′elllength = 46.5_{d} inches. I was also using a prefix form of base annotation, whereas I prefer subscript annotations now. I was also abbreviating the powerprefixes with uppercase vs. lowercase (e.g. unqua = U, uncia = u) whereas I prefer using special symbols now (e.g. unqua = u↑ , uncia = u↓ ). And of course, I have deprecated the ′kernel in favor of the ′morsel. (No more barleycorns, except as a footnote!) See Primel Metrology Wiki for more uptodate information.
Primel Length UnitsThe Primel base unit for length, the ′lengthel, is derived by taking the product of the ′speedel and the ′timel. This represents the distance traveled in z42 triciaseconds by an object moving at very close to 1 kilometer per hour. The resulting length is a bit smaller than an SI centimeter: about 8 millimeters or z5/14 of a customary inch. For those accustomed to base units of length being at the scale of the customary foot or the SI meter, this may appear at first glance to be a rather small unit to serve as the basis for a system of measure. However, note that historically the centimeter itself actually served in such a role, as a foundation for the CGS (centimetergramsecond) system, before that was supplanted by the MKS (meterkilogramsecond) system, now known as SI. The centimeter was, and still is, eminently serviceable as a unit of measure, and we shall see that the ′lengthel is at least as serviceable. In fact, when its dozenal powers are considered along with it, they turn out to constitute a very useful suite of length units. Here are the unqual powers of the ′lengthel:
The ′lengthel is a very close approximation of the line spacing of standard ruled paper, being almost exactly intermediate between the spacing of wideruled/legalruled paper (zE/28 inch) and mediumruled/collegeruled paper (z9/28 inch). This would suggest ′spacing as an apt colloquialism for this unit. One result of this is that if notebook paper were ruled with ′lengthelspaced lines, then quoting the number of lines per page would express the page's size in ′spacings. (Not counting header space at the top of the page, of course.) Another consequence is that existing standard ruled paper makes a fairly good approximation of a Primel ruler, which you can use to get a feel for how everyday objects would be measured. [Note: I am deprecating the previous colloquialism, "′line", for the ′lengthel. The name "′line" should be reserved for the ′unciathumb, an approximation for the customary line, which is one twelfth of an inch.] The ′lengthel is for instance about the width of standard 8 mm film, such as was used for the Zapruder film, or Super 8 mm film as was featured in the Spielberg movie Super 8. (However, I would not suggest giving it the colloquial name "zapruder" or "spielberg"!) The ′unqualengthel, a dozen ′spacings, approximates the traditional 4inch "hand" measure, and so can be called a ′hand. This is also remarkably close to a decimeter. This correspondence will prove important later when we derive volume and mass units. It is an interesting coincidence that (decimal) d10 centimeters, the basis for the liter and the kilogram, is almost exactly equal to (dozenal) z10 ′spacings, which will be the basis for the ′triquavolumel and the ′triquamassel. The ′biqualengthel, a dozen ′hands, makes a somewhat longish, but still quite serviceable, "meter" or "yard", and can play the same role as these units. Actually, it better approximates the English d45inch "ell" measure, so giving it the colloquial name ′ell is very appropriate. In fact, if we pronounc this "primeell", then it becomes a pun on the name of the whole system of measure! As an example, let's take a page from the old adage "mankind is the measure of all things". Here's a comparison of average heights in the US in SI, Conventional, and Primel units:
Which of these units is the best scale for measuring human proportions? Are kernels the best since they let you express human heights to three digits as whole numbers without fractions, or are ′ells better since they let you deal with smaller numbers, though with more fractional digits? Some of this is a matter of taste. Luckily, there are units for each of these scales, so we can try them all out for size and defer making a decision about this until later. The ′triqualengthel, a dozen ′ells, is about d14 meters or d47 feet. This is about d71% of a traditional English chain. Although this is a rather loose fit, we could perhaps coopt this name and give this unit the colloquialism ′chain. This might be a useful unit for architectural or civil engineering measurements. The ′quadqualengthel, a biqua (z100) of ′ells, is about d170 meters, or d559 feet. This is about d85% of a traditional English furlong, or d97% of an ancient Greek stadium (Olympic). The colloquialism ′stadium wouldn't be out of the question. This might be a good unit of measurement for land surveying or measuring city blocks. The ′pentqualengthel, a triqua (z1000) of ′ells, is almost exactly 2 kilometers. This explains why the ′velocitel is almost exactly 1 kilometer per hour: Since an unciaday is a ′pentquatimel, traveling a ′pentqualengthel in that time is equivalent to 2 kilometers in 2 hours = 1 kph. This distance also fairly approximates the statute and nautical miles; it is a somewhat bigger brother of both, but not radically so. Hence, it makes a fine unit for measuring geographic and travel distances. It could be given the colloquialism ′triquaell, but with a little worderosion this could be reduced to ′trekel, which would convey the sense of measuring travel distances. The ′hexqualengthel, a dozen ′trekels, is around two dozen kilometers or fifteen miles. This is about a day's march for an army on the move. An entire day moving at 1 ′velocitel covers this distance. A real army would of course make better time when actually marching, however they would no necessarily march around the clock; accounting for sleep and logistics, the pace would average out to this. Therefore, calling this distance a ′march makes for an apt colloquialism. Here are some possible auxiliary units using multipliers on the unqual powers to approximate other traditional units. However, these seem more trouble than they're worth, because the colloquialized unqual powers already seem useful and intuitive enough:
[TBD: Talk a bit about each of the colloquialisms. Fill in the higher powers up to the limit of the known universe, and take the uncial powers down to the Planck distance. Create entries for 1 astronomical unit (′astronomel? ′interplanetel?) and 1 light year (′interstellarel?).] 

Kodegadulo 
Posted: Apr 14 2013, 05:40 AM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
I thought I should pick up where I left off last year and resume developing the Primel metrology. I did a bit more fleshing out of the Primel Length Units (just above this post).

Kodegadulo 
Posted: Apr 14 2013, 12:42 PM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Did a bit more work on the Primel Length Units:

Kodegadulo 
Posted: Apr 14 2013, 04:49 PM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
I'm rethinking the colloquialisms for the Primal Time Units. I think the unciaday really needs a compelling colloquialism, one that is not derivative of "hour" like "bihour" or "duor". It probably should somehow derive from the Latin uncia in the same way that English ounce and inch did, but with a sense of "time of day". (The ancient Greek for "time of day" was in fact hora (ὥρα), whence English hour. Originally it had only a vague sense that could have covered any portion of a day (or even "season"), but of course it was coopted centuries ago for the specific meaning of "semiunciaday".) Hmm, if we combine "when" with "ounce", we could call the unciaday a "whence". But that won't work because "whence" means "from where", or "from which", not "from when". I've already got something I like for the triciaday: the "trice". I toyed with simply calling it a "′minute", since at d[50] (z[42]) seconds, it's very close to the sexagesimal minute. But "trice" is nice because it's already a perfectly good English word meaning a minute ("mynewt") amount of time, without simply aping the word minute ("minnit"). And of course it carries the sense of "threeness" coming from it being at once the triqua of the ′timel and the tricia of the day. It could even be interpreted as referring to the fact that you get it by dividing a day dozenallythrice. Well, you get the unciaday by dividing a day dozenally, once. So perhaps we need a word that combines the sense of "once" and "uncia". "Unce"? Hmm. How about the biciaday? It's a decaminute, or "temin". However, it makes no sense to give it a colloquialism that mentions not only the nondozenal base ten, but also the nondozenal sexagesimal minute. So we need something else. Well, you get a biciaday by dividing the day dozenally, twice. But "twice" and "trice" are too close together in sound and could be easily confused, especially with certain British accents and certain speech impediments. But if an unciaday is an "unce", and a triciaday is a "trice", then perhaps a biciaday should be ... a "bice"? Hmm. What about plurals of these words? Let's try them out: "There are one dozen trices in a bice, one gross trices in an unce, and one zagier trices in a day. There are one dozen bices in an unce, and one gross bices in a day. There are one dozen unces in a day. I work four unces a day, although often as much as five or six unces, but only get three bices for lunch, or equivalently, threezen trices." Meanwhile, I'm secondguessing using "twinkling" as a colloquialism for the ′timel. It may be more appropriate for the ′unquatimel instead. A "twinkling" is defined as "the time required for a wink". At approximately a third of a second, the ′unquatimel is about right for that. So I need a different colloquialism for the ′timel. I'm thinking now it should be the "jiffy" because that has a nonspecific meaning of a very short period of time. It's used technically to indicate specific tiny amounts of time, but at wildly different scales in different fields of science and engineering. So perhaps I can coopt it for the ′timel, especially if I cast it as the "′jiffy". I don't have anything good for the ′biquatimel. It's z[4.2] seconds long. About the time needed to breathe in an out when at rest. Call it a "breathing"? So what have we got? A dozen jiffies in a twinkling. Thoughts? Suggestions? 
Kodegadulo 
Posted: Apr 14 2013, 09:36 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Area UnitsThe Primel base unit for area, the ′areael, is derived by squaring the ′lengthel. This results in a square approximately 8 millimeters, or 5/14_{z} of a customary inch, to a side, equivalent to about 0.6741_{d} square centimeters or d0.1045 square inches. A square centimeter is equivalent to about 1.483_{d} (1.597_{z}) ′areaels. A square inch is approximately 9.57_{d} (9.6X_{z}) ′areaels. Just as for the ′lengthel, the ′areael might seem rather small for a base unit of measure. But quadrilleruled paper marked off in ′areaels would be quite useful for drafting and so forth. And when the ′areael is considered together with its dozenal powers, the suite of units proves to be useful for a variety of purposes: Here are some unqual powers of the ′areael:
The biqua′areael is one square ′hand, and might be referred to colloquially as a ′handarea. This is almost exactly one square decimeter (about d97 square centimeters) or d15 square inches. This unit might be good for measuring surface areas of everyday objects such as furniture and equipment. A square decimeter is approximately d1.03 ′handareas. A square foot is about d9.57 ′handareas. The quadqua′areael is one square ′ell, and might be referred to colloquially as an ′ellarea. This is approximately d1.4 square meters, or d15 square feet, or d1.67 square yards. This unit might be good for measuring floor plans, floor covering, and so forth. A square meter is about d0.715 ′ellareas. A square yard is about d0.598 ′ellareas. The hexqua′areael is one square ′remulcum, and might be referred to colloquially as a ′remulcumarea. This is approximately d2.01 ares, or d240.75 square yards. This unit might be good for measuring architectural plots for building and landscaping plans, smaller farming properties, and so on. A hectare is approximately d49.7 (z41.8) ′remulcumareas. An acre is about d13.96 (z11.E6) ′remulcumareas. The octqua′areael is one square ′stadium, and might be referred to colloquially as a ′stadiumarea. This is approximately d2.9 hectares, or d7.2 acres. This unit might be good for measuring larger farming properties, institutional building plans, city block maps, etc. A square kilometer is about d23.96 (z1E.E6) ′stadiumareas. A square mile is approximately d62.05 (z52.07) ′stadiumareas. The decqua′areael is one square ′dromicum, and might be referred to colloquially as a ′dromicumarea. This is approximately 4 square kilometers or d1.6 square miles. This unit might be good for measuring area on maps at urban and regional scales. The unnilqua′areael is one square ′itinerum, and might be referred to colloquially as an ′itinerumarea. This is approximately d601 square kilometers or d232 square miles. This unit might be good for measuring area on maps at national or continental scales. 

Kodegadulo 
Posted: Apr 17 2013, 04:29 AM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Finished writeup on Primel Area Units and linked to it from the table in the original post.

Kodegadulo 
Posted: Apr 17 2013, 12:54 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Time UnitsNOTE: This post supplants this previous post and institutes some changes to the colloquialisms. I'm keeping the old post for historical reasons rather than editing it. The mean solar day is a fundamental reality of Primel, just as it is for TGM. However, Primel will use a round dozenal power of the day, the hexciaday, as its base unit of time, the ′timel. This contrasts with TGM, which first divides the day in half, and then takes the pentcia of the semiday as its base time unit, the Tim. As a consquence, the ′timel is equivalent to onesixth of a Tim. This makes the ′timel a very fleeting moment of time, just beyond human perception. I have proposed calling it, colloquially, a ′jiff. Nevertheless, it is a useful quantity for precision scientific and engineering purposes, and its scale will have interesting effects on the rest of the Primel metrology. On the other hand, the unqual powers of the ′timel, starting with the ′unquatimel, do fall within the human scale. The table below shows a range of dozenal powers of the ′timel, from ennqua down to enncia. The ′timel itself is highlighted in blue, and the "human scale" powers up to the full day are shown in green. Each of these is equivalent to an uncial power of the day, and these equivalents can be used as synonyms. One useful feature to note at the top of the scale is that higher powers of the ′timel correspond to whole powers of the day, so there is a seamless transition from largescale measures of time based on the day and smallerscale measures of time. Prefixes indicate base: d = decimal, z = dozenal. See Radix Prefixes for more details.
The ′unquatimel is a dozen jiffies, equivalent to 2 Tims or about a third of a second. It is approximately the time needed for a wink. Therefore an appropriate colloquialism for it may be the twinkling. It is also equivalent to a beat of a metronome in the presto range. Counting ′unquatimels in threes approximates the tempo of a Viennese waltz. The ′biquatimel is a dozen twinklings, equivalent to 2 unquaTim or z4.2 seconds. The ′triquatimel is a dozen The ′quadquatimel, or biciaday, is a dozen ′trices, equivalent to 2 triquaTim or ten conventional minutes. The ′pentquatimel, or unciaday, is a gross of ′trices, equivalent to a long hundred (d120) conventional minutes, which is the same as 2 conventional hours. Using SDN prefixes, we might call the former a "decaminute" and the latter a "bihour", but less derivative expressions might be more appropriate to colloquialize these units. First attempt: Second attempt: Third attempt: A good nickname for the unciaday might be the ′stound. "Stound" is an archaic English word with roots hearkening back to Old English. It was actually the word for "hour" or "time of day" (cognate with the German Stunde), until the Norman conquest supplanted it with "hour" borrowed from the French. The biciaday might be nicknamed a ′bout. Some of the definitions of "bout" include "period; session; spell" and "a turn at work or any action". The fast hand on the DSGB clock suffers a "bout" of a dozen spins during one biciaday. In a Primel world, when you want to take a break, instead of telling everyone to "take ten" (minutes) or even "take a dozen" (′trice), you could say "take about a ′bout". Although the TGM time units are not whole dozenal powers of the ′timel, they are all a simple multiple of one, so we could certainly incorporate them into Primel as auxiliary units:
Here are a few additional auxiliary units that are all interesting multiples of some dozenal power of the ′timel:
A Perennial Calendar can be constructed where every year and month starts on the same day of the week, where every year and month contains a whole number of weeks, and where a leap year adds a leap week onto the last month of the year, rather than a leap day in February. The pattern of leap years would be quite different, of course. When such a calendar is interpreted in dozenal, there's a nice sort of correspondence between how each month is either z24 or z2E days and how each year is either z264 or z26E days; or equivalently, how each month is either 4 or 5 weeks and how each year is either z44 or z45 weeks. (This is essentially a dozenalization of Irv Bromberg's Symmetry 454 Calendar, which was discussed along with other perennial calendars in this thread.) [z] The following is all in dozenal.
Additional material at: Names for Some Fractions of the Day 

Kodegadulo 
Posted: Apr 17 2013, 11:43 PM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Discovered that one version of the ancient Greek stadium measure is very close to the length of the ′quadqualengthel, much better than the English furlong. So replaced the colloquial name to be ′stadium. Also the ′octquasquarel (the square ′quadqualengthel) is now a ′stadiumsquare.

Leopold Plumtree 
Posted: Apr 20 2013, 01:13 AM

Regular Group: Members Posts: 346 Member No.: 59 Joined: 26May 06 
Nice to see the Primel system moving forward! I'm bit of a fan.

Kodegadulo 
Posted: Apr 21 2013, 11:24 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Volume UnitsThe Primel base unit for volume, the ′volumel, is derived by cubing the ′lengthel. This results in a cube approximately 8 millimeters, or z[5/14] of a customary inch, to a side, equivalent to about d[0.5535] milliliters, or d[33.78×10^{3}] cubic inches, or d[18.72×10^{3}] U.S. customary fluid ounces, or about a 1/9 of a U.S. customary teaspoon, or about z[54] hexciaVolm. A milliliter is equivalent to about d[1.807] (z[1.982]) ′volumels. A cubic inch is approximately d[29.61] (z[25.73]) ′volumels. A U.S. customary fluid ounce is equivalent to about d[53.43] (z[45.52]) ′volumels. A U.S. customary teaspoon (approximately 5 ml) is about 9 ′volumels. A TGM Volm is equivalent to about z[23,000] ′volumels. (This makes sense because this z[23,000 = 30^{3}], and the TGM Grafut is equivalent to about z[30] ′lengthels. Just as for the ′lengthel, the ′volumel might seem rather small for a base unit of measure. However, there are certain commonplace volume measurements at the fine end of the scale, such as measuring quantities of liquid medications, that it would be perfectly suitable for. And when the ′volumel is considered together with its dozenal powers, the suite of units proves to be useful for a variety of purposes:
The ′triquavolumel is one cubic ′unqualengthel, or cubic ′hand, and so might be referred to colloquially as a ′handvolume, or ′handvol for short. As a result of the ′hand being such a close approximation of the decimeter, the ′handvol is remarkably close to one liter: about d[956] milliliters. More interestingly, the ′handvol is intermediate between a liter and a U.S. customary quart, and is actually extremely close to the latter: about d[1.01] quart. This makes it an even better approximation to a quart than Pendlebury's "quartol" (hexabiciaVolm). Indeed, if a liter is (as the old adage says) "a leeter bit more than a quart", then a TGM quartol is a "leeter bit more again". In fact, if the TGM Gee had been identical to the ′gravitel (which equals the SI standard gravity), then the quartol would have been exactly 9/8 of a ′handvol (z[1.16] ′handvols). This makes the TGM quartol nearly d[8%] larger than a liter, and nearly d[14%] larger than a quart. Whereas the ′handvol is only d[1%] over the quart, and less than d[5%] under the liter. All in all, users of both the SI and U.S. customary systems may be a "leeterbit" happier adjusting to the ′handvol than to the TGM quartol. If the ′triquavolumel is so close to the liter and the quart, then why not colloquialize it as either a "primel liter" or a "primel quart", or even as both? Well, first of all, such names would imply that Primel units are somehow derivative of either customary or SI units, but in fact they are quite independent. It would be preferable to relate the ′unqualengthel, and by extension the ′triquavolumel, to some object such as the human hand which provides an intuitive sense of scale. Second, the "quart" itself derived its name from the fact that it is a quarter of a U.S. customary gallon. Why should the name of a Primel unit make reference to a fractional relationship between units in another metrology? We could just as easily stand this on its head and characterize the gallon as being a U.S. customary "quadrahandvol". In fact, let's relate some other U.S. customary measures to the ′volumel and the ′handvol:
Moving up the scale: The ′quadquavolumel, colloquially known as the ′unquahandvol, is about a dozen liters or 3 U.S. customary gallons. This is about the amount of water per flush in a typical oldstyle (pred[1990]s) flush toilet. The ′pentquavolumel, colloquially known as the ′biquahandvol, is about a gross liters or three dozen U.S. customary gallons. This is about the capacity of a typical tall kitchen trash bag, or about the volume of water needed to fill a typical bathtub. The ′hexquavolumel is one cubic ′biqualengthel, or one cubic ′ell, and so might be colloquialized as an ′ellvolume, or ′ellvol for short. This is about d[1.65] cubic meters, or d[2.16] cubic yards. This unit may be appropriate for measuring large industrial vats or tanks. The ′ennquavolumel, is one cubic ′triqualengthel, or one cubic ′chain, and so might be colloquialized as a ′chainvolume, or ′chainvol for short. This is about d[2856] cubic meters, or d[3735] cu yards. The ′unnilquavolumel is one cubic ′quadqualengthel, or one cubic ′stadium, and so might be colloquialized as a ′stadevolume, or ′stadevol for short. This is about d[4.935] million cubic meters, or d[6.455] million cubic yards. The ′untriquavolumel is one cubic ′pentqualengthel, or one cubic ′trekel, and so might be colloquialized as a ′trekelvolume, or ′trekelvol for short. This is about d[8.528] cubic kilometers, or d[2.046] cubic miles.
Other interesting posts about volume units: 

Kodegadulo 
Posted: Dec 15 2013, 06:05 AM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
After neglecting this project for too long, I figure it's high time I pick up where I left off. Note that I've done some sprucing up of the previous posts in the chain, so it may be worth it for you to look them over again. Primel Mass UnitsThe Primel base unit for mass, the ′massel (′Msℓ), is the mass of one ′volumel of water at maximal density. This makes the ′massel equivalent to about d0.5535 grams, or d0.01952 ounces, or d8.542 grains. Since the ′volumel is colloquially a cubic ′kernel, or ′kernelvol, the ′massel can be colloquialized as a ′kernelmass. At a bit over a half a gram, the ′massel shares with the gram the disadvantage of being relatively small for a base unit of measure. Even so, it certainly has applications for fine measurements of mass. Furthermore, the ′massel's third dozenal scaling, the ′triquamassel (′TMsℓ), turns out to be remarkably close to the gram's third decimal scaling, which is of course the kilogram. At about d956.4 grams, it is less than d5% off from the kilogram. This makes it at least as applicable to everyday uses as the kilogram is. People accustomed to using SI units would find it easy to adapt to using ′triquamassels. Moreover, by being a little less than the kilogram, the ′triquamassel comes even closer than the kilogram does to being a double pound. At d2.109 pounds, or d33.74 ounces, it comes within about d5% of a bipound. Simply dividing customary avoirdupois masses by two provides a reasonable rough approximation of the equivalent in ′triquamassels. So users of the avoirdupois system would also find it relatively easy to adapt to using ′triquamassels. So should we colloquialize the ′triquamassel as a "primel kilogram", or a "primel bipound"? That would imply that the primel unit is somehow based on the kilogram or the pound, but this is not the case at all. A better choice would be to exploit the fact that the ′triquamassel is the mass of a cubic ′hand, or ′handvol, of water. So by extension we could call it a ′handmass. Here are a number of dozenal powers of the ′massel:
The ′quadquamassel (′QMsℓ) is noteworthy in being quite close to d25 pounds, which is a handy round number for users of avoirdupois units. The ′hexquamassel (′HMsℓ), being three dozenal orders larger than the ′triquamassel, could play the same role as the U.S. or metric ton, but as a somewhat larger brother to both. But rather than colloquially call it a "primel ton", we should take note that it is the mass of water in a cubic ′ell, or ′ellvol, and therefore call it a ′ellmass. We can also relate the ′massel and ′handmass to the U.S. customary pound and ounce; and we can exploit the relationship between mass and volume to derive some additional colloquial unit names:


Kodegadulo 
Posted: Dec 15 2013, 01:57 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Units of Force or WeightThe Primel base unit for force, the ′forcel (′Fcℓ), is the force that imparts an acceleration of one ′accelerel upon a mass of one ′massel. Since force and weight are synonyms for the same kind of quantity, this unit can also be called the ′weightel (′Wtℓ), and can be described as the weight that a one ′massel object has within a one ′gravitel gravitational field. This makes the ′forcel or ′weightel equivalent to about d5.24279 millinewtons, or d0.5535 gramsforce, or d0.01952 ouncesforce. Since this is the weight of a cubic ′kernel of water (in a standard Earth gravity), we could colloquialize this force unit as a ′kernelforce or ′kernelweight. Indeed, because the Primel system equates the ′accelerel with the ′gravitel, there is a onetoone correspondence between each of the dozenal scalings of the ′massel and the same dozenal scalings of the ′forcel or ′weightel. So all the colloquializations for the mass units can be extended to the force/weight units:
We can do similar with weights associated with common U.S. customary volume measures:


Kodegadulo 
Posted: Dec 15 2013, 05:39 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Units of Work or EnergyThe Primel base unit for work, the ′workel (′Wkℓ), is the work performed by applying a force of one ′forcel over a distance of one ′lengthel. Since work and energy are synonyms for the same kind of quantity, this unit can also be called the ′energel (′Ngℓ). This makes the ′workel or ′energel equivalent to about d44.566 microjoules, or d445.66 ergs. Since this is, colloquially, the work performed by applying one ′kernelforce over a distance of one ′kernel, we could colloquialize this as one ′kernelwork or ′kernelenergy. Compared to the SI joule, the ′workel is quite small. But compared to the old CGS unit of energy (the erg), it's actually rather large. Of course, those used to thinking in joules may find this unit inconvenient except for fine energy measurements. However, we have an easy out for this, by dozenally scaling the ′workel using SDN prefixes. Consider the ′quadquaworkel. We could characterize this as the work performed by applying one ′handforce (′triquaforcel) over a distance of one ′hand (′unqualengthel). So it would be very appropriate to call this unit, colloquially, a ′handwork. As it turns out, this unit happens to be quite close to one joule! (It's equivalent to about d0.9241 J.) So the ′quadquaworkel would be approximately as convenient to use as the joule. However, it's arguable that even the joule is rather too small a unit for many applications. For instance, we have to go to kilojoules in order to describe the energy in just one dietary calorie (approximately d4.184 kJ). And we count a daily diet in thousands of such calories. Even more poignantly, we never hear domestic or commercial energy usage expressed in joules. Instead, it's usually expressed in kilowatthours. One kilowatthour is equivalent to d3.6 megajoules  more than 6 decimal orders of magnitude over the base unit! This scheme of leveraging a largish power unit multiplied by a largish time unit certainly can produce a big scaling up of a smallish energy unit. Unfortunately, doing this in SI makes the kilowatthour an oddball unit, because the large time unit it is based on (the hour) is not a simple decimal power of the base time unit (the second). Fortunately, TGM and Primel don't need to suffer this problem. We could certainly measure energy using Povhours or ′handpowerdays. However, these would be indirect ways of applying dozenal powers to the base units, and this can be done more simply and directly with SDN prefixes: The Povhour would be just another name for the quadquaWerg. Likewise, the ′handpowerday would be just another name for the ′hexquahandwork or ′decquaworkel. This unit turns out to be equivalent to about threequarters of a kilowatthour (approximately d766.50 Whr), so it would be useful for measuring energy consumption. Notice that the ′ellwork, the energy necessary to take one ′ellmass (d1.653 metric tons) and raise it by one ′ell (d1.182 meters) against one standard ′gravitel, is only d19.162 kilojoules  which is only d4.58 (kilo)calories! That's about the chemical energy in a quarter of a packet of sugar! Just goes to show how "compact" chemical energy is compared to simple kinetic energy or gravitational potential energy. Certainly if one considers the amount of kinetic energy that can be unleashed by igniting a small amount of some explosive chemical, this makes a lot of sense.


Kodegadulo 
Posted: Dec 15 2013, 11:49 PM


Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Primel Power UnitsThe Primel base unit of power, the ′powerel (′Pwℓ), is a rate of energy consumption equal to one ′workel in each ′timel (′Wkℓ/′Tmℓ). Colloquially, this is equivalent to a rate of one ′kernelwork per ′jiffy, so we could give this unit the colloquial name ′kernelpower. This makes the ′powerel equivalent to about d1.5402 milliwatts, or d[15.402 kiloergs/second. As with other Primel units, the ′powerel is relatively small compared to the analogous SI unit (the watt), but quite large compared to the equivalent CGS unit (erg/second). Although the ′workel was even tinier compared to its SI analog, being in the microjoules, the ′powerel has gained some ground simply because we divide by the ′jiff, and the ′jiff is tiny compared to the SI second. But once again, we can mitigate any size inconvenience by using SDN prefixes to scale the ′powerel. For instance, the ′triquapowerel (′TPwℓ) is equivalent to d2.6615 watts. This is a rate of energy consumption of one ′quadquaworkel (′QWkℓ) per ′unquatimel (′UTmℓ). Colloquially, this is a rate of one ′handwork per ′twinkling, so it can also be called a ′handpower. As an example, standard d40 watt, d60 watt and d100 watt light bulbs could be approximated as oneandaquarter dozen (z13) ′handpower, oneandseveneighths dozen (z1X.6) ′handpower, and threeandoneeighth dozen z31.6 ′handpower. Or perhaps these could be rounded to z10 ′handpower, z20 ′handpower, and z30 ′handpower, respectively. The ′hexquapowerel, known colloquially as the ′ellpower, is the rate of energy consumption needed to take an ′ellmass (d1.652 metric tons) and raise it in a one ′gravitel field to a height of one ′ell (d1.1823 meters) within one ′biquatimel (


Kodegadulo 
Posted: Dec 16 2013, 11:49 AM

Obsessive poster Group: Moderators Posts: 4,184 Member No.: 606 Joined: 10September 11 
Note: I've updated the summary table in the original post:

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