dm-kg system

If you live in a metric country, and want to get to use dozenal, then this system gives you access to large numbers without too much trouble.

Counting does not really give you to really big numbers. This is why having good access to a ready source of simple numbers to convert is a good idea. We can use Wilberforce-Mann's names to distinguish these.

1. Time. Here we divide the day to 12 hours of 144 minutes of 144 seconds.

2. Length: LINN = 1 dm. Many of the values can easily be converted to decimetres, and converted to dozenal from that. So seeing 1.82 metres gives 18.2 dm = 16.3 Linn. Long distances are converted on the value that 1 mile = 1 D4 Linn = 2.0736 km. The sign coming up saying Xyz 40 km, gives 20.0 = 18 z Miles.

3. Speed. Since the Kine or Linn per second, becomes 2.0736 km / 2 hours, those black numbers in the red circle, etc, are simply converted. 60 km/h = 50 z KINE. It's a one-for one conversion.

4. Volume. The Litre is unchanged, but becomes a CAPP. A cup is 0.25 L = 1/4 L = 300 'millicapp'.

5. Weight. The Chogg or Pondd is a kilogram, so masses in kgs are converted as is. A weight of 150 Kg becomes 106{z} chogg.

6. Money. The money has been largely debased since the seventies, but one can reflect this by supposing 1 penny = (something near the us$ or €). You then are converting something like $ straight as a dozenal number. I use the same system with £sd where 1d = 1 $AU.

Of the first point:

wendy.krieger wrote:1.  Time.  Here we divide the day to 12 hours of 144 minutes of 144 seconds.

While by the context what was meant can be understood, the words "hour", "minute", and "second" have been recycled to mean different periods of time, so that here "hour" meant a double hour, a "minute" was fifty seconds, and a "second" was 25/72 conventional seconds.

In the second point:

wendy.krieger wrote:1.82 metres gives 18.2 dm = 16.3 Linn.  Long distances are converted on the value that 1 mile = 1 D4 Linn = 2.0736 km.  The sign coming up saying Xyz  40 km, gives 20.0 = 18 z Miles.

In 18.2 dm, the two tenths of decimal 0.2 convert to the nearest two twelfths of dozenal.

"D4" meant twelve to the power of four.  By "mile" was meant twelve to the power of four times the unit of length, so this as 2.0736 kilometres is more than a quarter part bigger than a conventional mile of about 1.6 kilometres, although there are other kinds of mile such as a nautical mile which is closer. The conversion of halving the kilometres and writing the resulting number dozenally comes about by the fourth power of twelve being the choice of rounding approximation to twice ten thousand, that is, 12^4 nearly equals 2 * 10^4. This mathematical property applies to other metric choices for the basic unit of length, such as five centimetres times the fourth power of twelve being near a kilometre, so it is not unique to this system. Other approximately simple ratios of powers of the two bases are possible and useful in rounding, such as 2 * 12^9 ~= 10^10 or 12^13 ~= 10^14, though these would be appropriate for the design of the basic units if the sensitivity or granularity of human discrimination of quantities were finer.

wendy.krieger wrote:3.  Speed.  Since the Kine or Linn per second, becomes 2.0736 km / 2 hours, those black numbers in the red circle, etc, are simply converted.  60 km/h = 50 z KINE.  It's a one-for one conversion.

This conversion is an approximate rule of thumb. Admittedly, however, it is an advantage of this proposal.

It is a matter of prioritizing which decimal metric values would convert exactly by a unitary factor to dozenal. Many dozenalists would recoil at the proposal of using a metric quantity such as a decimetre because of how the metre is derived by a decimal division of the polar circumference. Consequently, there would need to be an attempt to justify this length by a dozenal derivation.

This particular system was more designed for someone without the skills to make a decent dozenal system, to still participate in converting random numbers from decimal to dozenal, and to build some sort of dozenality about it.

An hour is simply a time unit struck by a bell.  Before the europeans arived in earnest, the Chinese had a 10-hour day, and the Indian bell or ghurry was 1/60 day.  A minute is a little division on the clock face.  It really only came to the fore when we started using the clock-face.  Second, as it always has been, is simply the second division.  Stevins used the word to refer to the second decimal column.

Of course, this particular system really is not intended to be a heavy-duty replacement.  You need to consider the various options that different metrologies offer.  But it is a thing that people in metric countries can get to think of dozenal units, and the units are not that far off either Essig's metric system, or my own dozenal COF.  

Part of getting to know a base is to be able to visualise numbers as measures, and this is a pretty good way to start.  This particular system preserves, for example, specific gravity as 1, and gravity as near 10 (z), which is pretty much like metric:  1 Newton = 0.102 kg (decimal), and 1 force = 0.1 Pondd (dozenal).

It is interesting to note that the core linear part of the ancient sumerian system, can be constructed around the decimetre too.

Mile simply means 'thousand'. In the sense of length, it is a thousand smaller units. Here the smaller unit is 1.2 metres or an aune, and 1728 aune make a mile. The Russian immigrants in my cousin's family translate the 1.6 km unit as a verst, even though the russian unit was 1.066 m, nearer the km. Metric had no problems adopting the 'ton', even though it is not 2000 lb.

There are a certain group who think that new units need new names, and others who are quite happy to recycle names, especially if the construction of the units are preserved. I am one of the latter. So, for example, a 'mile' is a unit that heads the thousand-measure, the nautical mile is 1000 nautical fathoms (of 72.96 BI inches), the twelfty mile is 1.00.00 units of six inches, and the dozenal metric mile is 1000{z} aune. The metric mile is 1000 paces of 5 ft of 300 mm, or 1.5 km. It is so used as such.

wendy.krieger wrote:This particular system was more designed for someone without the skills to make a decent dozenal system
[...]
Of course, this particular system really is not intended to be a heavy-duty replacement.

A dozenal system should be as easy to use as possible. To be introduced, this would mean retaining as many of the most commonly used existing legal standards as possible. A dozenal system that does not have simple whole number conversion factors from the common legal standards would not be as  plausible a proposal.

There is some flexibility in the choice of terrestrial gravitational acceleration. A system can be designed so as to make the unit of length exactly equal a common unit. At the moment, the unit of length in the Primenote metrology using a sextic dozenth of the day for the temporal unit is near to a twelfth of a decimetre. By changing the gravitation, this might be better made to exactly equal the decimetre.

Another option is to divide a terrestrial circumference by a power of the dozen. Using 6371 kilometres as a radius of the Earth, multiplying by twice pi to give a circumference, and dividing by twelve to the power of eight gives a unit of length about 9.31 centimetres, probably too much less than a decimetre considering how the error multiplies in the volume for example.

wendy.krieger wrote:gravity as near 10 (z), which is pretty much like metric:  1 Newton = 0.102 kg (decimal), and 1 force = 0.1 Pondd (dozenal).

Converting 9.8 metres per square second into the dozenal unit of length per square dozenal unit of time, done by 98 decimetres divided by the square of 72/25 temporal units is about 11.8 lengths per square times, near twelve.

The force is not the mass producing it in the gravitational field of the Earth. The force is the mass times the acceleration. The magnitude of the mass required for one unit of force is therefore the reciprocal of the acceleration. So, for one Newton, the mass required is 1/9.8 kilograms. To produce the unit of force in the dozenal metrological system, a mass of about 0.085 unit masses, near a twelfth of a unit mass, would be required.

wendy.krieger wrote:It is interesting to note that the core linear part of the ancient sumerian system, can be constructed around the decimetre too.

Years ago I read the beginning part of the book called "Civilisation One" by Christopher Knight which deals with this.

Phaethon wrote:the unit of length in the Primenote metrology using a sextic dozenth of the day for the temporal unit is near to a twelfth of a decimetre. By changing the gravitation, this might be better made to exactly equal the decimetre.

Twelve times the multiple of the acceleration 9.8 metres per square second by the square of the time unit gives 12 * 9.8 * (24 * 60^2 / 12^6)^2 ~= 0.09895 metres. If this were to be exactly a decimetre, the acceleration would have to be 0.1 metres * (24 * 60^2 * 12^-6)^-2 /12 ~= 9.95 metres per square second, which is above the maximum of the range found on the surface of Earth.

It is worth noting that Essig and Crosby used simple metric names (like km, kg), for their units, the units coming closest to the SI at the dm-kg points.  So much so, that we could use a common conversion table for them all: as follows, with x as small value.  In any case, putting X=1 will give a good approximation.

km	2.0736x km
hm	172.8x m
Dm	14.4x m
m	1.2x m
dm	100x mm
cm	8.33333x mm
mm	0.694444x mm

x of Essig system = 0.930272,  so that the earth circle = 10000 km (E)
x of Crosby system = 0.985268, so that g = 1 m/s², with 12^5 seconds in the day.

The ratio of these is 17/18, a factor noted in Pendlebury's TGM.

We can suppose a system where there are three competing sets of units:

 DM = dozenal metric, where x=1 in the table above.
 DN = dozenal nautical, or that of Essig's
 DG = dozenal gravitational, or Crosby's system.

To each of these, there is a parallel system, based on a foot of 3 dm.  

  perch = 3 m (3.6x m SI),  foot = 3 dm (300x mm SI),  inch = 3 cm (25 mm SI), and line 3 mm (2.0833 mm SI).

 The DN foot is the base unit of de Pujal's system.  It is very close to the spanish foot, or to 11 inches.  Churchwood used 11 inches, making the earth-circle 24883.2 miles.

 The DG foot is the base unit of Pendlebury's TGM (timm, grafoot, maz).

You can simply use all the units together, having on one side of the ruler, 12 inches, and the other side, 36 (30z) centimetres.

The C.O.F. system of Krieger is the DG cm-g-instant, where 12 instants make a second.  The DG dm.kg.s appears as the Linn-Pondd-Second system there.

The Primel system of Kodegadulo is the same as COF, to the extent of borrowing the temperature and electrical units from COF.  The DG dm-kg-s system appears as the hand subsystem there.  This system relies heavily on quantitels and prefixes, both considered bad moves.

A feature of the DG system, is that one has a range of 'traditional' units, which resolves down to simple numbers of COF units.  So a pressure given in PSI, gives 1 lb = 600 g, 1 inch = 3 cm, so it comes to 80 g/cm², but since a gram-force = a dyne, it gives 80 dynes/cm² or 80 bayre. [using cgs names for the cof names].

It is possible to select other base units far away from the dm-kg system, such as the light-second divided to 12^8 spans of 9.53 BI inches.  But that's a different story.

wendy.krieger wrote:The ratio of these is 17/18, a factor noted in Pendlebury's TGM.

This ratio approximates to that of a semitone. Perhaps the nautical and gravitational systems could be unified by a scale that catches the semitone. For example, using a binary power root of the base twelve, the cube or third degree \( 12^{3/{2^7}} \) of an increment of the scale approximates to the semitone ratio.

Overall, the summary was a satisfying explanation and introduction to many dozenal metrological systems. The reader just has to be constantly vigilant to interpret the recycled names of units according to how they have been defined.

wendy.krieger wrote:3 dm (300x m SI)

It appears this was supposed to have had mm typed for millimetres.

wendy.krieger wrote:12 instants make a second.

Seconds are redefined in the Opening Post of this topic as 12^-5 days.

wendy.krieger wrote:the light-second divided to 12^8 spans of 9.53 BI inches.

Again, the redefined second is 25/72 conventional seconds, so one conventional second is 72/25 = 2.88 redefined times. Thus, 2.88 times per second * 9.53 inches * 12^8 * 2.54 centimetres per inch divided by 100 for centimetres per metre give nearly 3 * 10^8 metres as the distance travelled per second by light.

It would be good if a dozenal unit of length could be derived through physics such as from the Planck length. A human scale unit could be in the region of an octalliad of Planck lengths, perhaps nine octalliads for about five metres, or four octalliads for 87 inches.