Dozenalizing Metric

On the Twelfty Online forum, in a topic on dozenal at https://www.tapatalk.com/groups/twelftyonline/dozenalising-the-metric-system-t24.html, Wendy decided that the appropriate size of unit of length at the human scale of measurement is on the order of the decimetre.

wendy.krieger Oct 03, 2018 wrote:The sorts of numbers one encounters in life-size objects are best expressed in decimetres,

The choice of sizes of base units of measurement may be argued by observation of the units of the decimal metric system that are most usually used on packaging of everyday commodities purchased by the ordinary consumer.

For volume, of the larger bottles of water and for petrol filling litres are seen, which are a thousand cubic centimetres, the cubic root of which is a length of one decimetre. Also used on the Continent on bottles are tens of the centilitre, which is ten cubic decimetres. By taking the cubic root of a typical volume, a suitable basic unit of length may be obtained. I do not see decilitres encountered. When millilitres are seen, this is going into the cosmetics and hygiene sectors and range for pharmaceutics or medical products, which is becoming technical or scientific and starting to be outside the scale of human size. Microlitres and smaller are certainly not everyday measures for ordinary purposes.

For mass, kilograms are used on larger grocery items such as boxes of cereal. A kilogram is the mass of a litre of water, so a decimetre as a basic unit again is suggested. Probably more common however are smaller or less heavy food items, such as jars of spreads, which are labelled in the hundreds of grams. The grams go down to the tens for sweet bars. Smaller than grams are hardly seen except for potent substances, which is in the technical or scientific and not ordinary everyday domain. Micrograms are not used typically except by professionals in science. At the larger end of the scale tonnes may be used industrially, but this goes beyond the scale that an ordinary person can gauge.

Lengths used for travel are kilometres, which are normally beyond human direct experience, being out of the reach of the body. Metres are commonly used of buildings. Decimetres are not spoken of directly. Centimetres in the hundreds are used for the heights of humans. Millimetres are used in engineering and industry, but they are too small to be judged by a human without instrument or ruler accurately.

So yes, a realistic human scale basic unit of length would be in the region of one to a hundred centimetres with some flexibility, and a decimetre falls into this range.

Phaethon wrote: a realistic human scale basic unit of length would be in the region of one to a hundred centimetres with some flexibility

The metre, while fine for length in itself, as a basic unit in a metrology with coherence based on the density of water is too large because its cube produces a thousand litres, which is too large for ordinary human experience. When a basic unit is being used, multiples rather than fractions of it are preferable, so a unit smaller than the most typical size measured would be better, and the basic unit of length would tend to be between about a decimetre and centimetre.

I designed many different measurement systems, in many different bases, and many different applications.  

When I decided to accelerate the creation of these systems, I made a careful study of what quantities really mattered in making a good system: get density and velocity right, and the rest pretty much falls into place.  In essence, atoms might be regarded as hard spheres, and solids from molecules to stars have a density not much different to water.  Also, velocity is closely related to temperature, so we have speeds of 300 m/s are related to gasses in the atmosphere.  A speed of 11,000 m/s is the escape velocity of the earth, so the molecules in the atmosphere generally do not escape from the earth.  

The standard systems, like the foot-pound-second and metre-kilogram-second, are derived from picking units mentioned in the act.  It's rather like picking a throuroughbread dog from the pound.  To this end, it turns out that the second is too long, but there is no real choice in the act for anything shorter.

The best one can do for metrics is dm-kg-ds, as proposed by Wm Moon in 1893.  But 'ds' is not in the act, so it really didn't come to much.  

In my dozenal C.O.F. system, i divide the day into 12 hours of 144 minutes, or 144 seconds, but this second is still too long.  Luckily an instant of 1/12 second works wonders.

I am always willing to listen to other people's ideas on these things, though.

wendy.krieger wrote:velocity is closely related to temperature, so we have speeds of 300 m/s are related to gasses in the atmosphere.  A speed of 11,000 m/s is the escape velocity of the earth, so the molecules in the atmosphere generally do not escape from the earth.

Hydrogen gas molecules escape, as do helium atoms which are not molecules, but I do not think of any other molecule lighter than methane on Earth in the atmosphere. Not too many lighter molecules come to mind, except borane and lithium and beryllium hydrides. Ionic forces could hold lithium hydride units together as a solid.

wendy.krieger wrote:i divide the day into 12 hours of 144 minutes, or 144 seconds, but this second is still too long.

Compared to 25/72 seconds, the reciprocal of 25/36 seconds in its small powers, notably the square and cube, gives near whole number conversion factors for mechanical and other derived unit quantities, which could be used as mental rules of thumb for translation between the existing metric and dozenalised metric without need for calculation devices.

Phaethon wrote:Compared to 25/72 seconds, the reciprocal of 25/36 seconds in its small powers, notably the square and cube, gives near whole number conversion factors for mechanical and other derived unit quantities, which could be used as mental rules of thumb for translation between the existing metric and dozenalised metric without need for calculation devices.

This quantity of time has been subsequently described as basic unit of time defining the Pendulum System , https://dozenal.forumotion.com/t23-pendulum-system, where units of length, mass, electrical charge, and moles were all derived using it. In that Pendulum, decimal powers of units of the Système International d'Unités (SI) are retained and can be converted to dozenal easily without conversion factors.

However, because of the sizes of units selected to have a dozenal basis of origination, for the magnitudes there can result some large positive or negative exponents of the base during the conversion, which can be dealt with by using scientific notation. Further, very small or very large sizes of the units of measurement themselves can be tackled by prefixes to the units.

Despite that very large or small orders of magnitude can be addressed by scientific notation and prefixes for power to units, it has been remarked that it would be more convenient if the occurrence of these orders could be avoided.

wendy.krieger on Mon Aug 12, 2019, https://dozenal.forumotion.com/t5-dm-kg-system#31 wrote: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.

It could be worthwhile investigating which selections of units from the Système International d'Unités would tend to produce manageable magnitudes or simple orders of the base and units in the human range of usability without prefixes.

Some studies have been mentioned on selecting appropriate units from the legislative acts:

wendy.krieger, 9:20 AM - Sep 25, #6, https://www.tapatalk.com/groups/twelftyonline/on-designing-new-systems-t47.html wrote:This little essay is not about setting the base units against any particular standard, but about the relation so that one does not involve large and small numbers like the CGS and FFF (furlong-firkin-fortnight) systems do. 

In practice, the base units are drawn from the WMA (Weights and Measures Act), so the choice here is hampered by selections in the act.

wendy.krieger, 9:37 AM - Sep 05, #1, https://www.tapatalk.com/groups/twelftyonline/on-designing-new-systems-t47.html wrote:The choice of Length, Mass, and Time as base units has nothing to do with physics or nature, but reflect instead that the metrological acts define these measures, along with capacity.

wendy.krieger, 9:38 AM - Sep 06, #3, https://www.tapatalk.com/groups/twelftyonline/on-designing-new-systems-t47.html wrote:the time is mismatched for the CGS, the velocity is something like 0.01 m/s, whereas the COF has a time-unit of 1/34.56 seconds, so its velocity is something like 0.288 m/s, which is a lot more practical.  The unit of energy in the CGS is 0.0000001 joules, where the cof unit is 0.001 joules.

In the Pendulum system, the basic unit of time was less than a conventional second, but the hectosecond is proposed for ease of convertion from metric units, and this caused powers of the units of the Pendulum system to result. It is claimed that there is a difficulty in part due to the basic unit of time, while it may be transiently brief by human understanding, being too long because of the powers it produces.

wendy.krieger on Thu 8 Aug 2019 - 9:05, https://dozenal.forumotion.com/t3-dozenalizing-metric wrote:The standard systems, like the foot-pound-second and metre-kilogram-second, are derived from picking units mentioned in the act. [...] To this end, it turns out that the second is too long, but there is no real choice in the act for anything shorter.

wendy.krieger on Thu 8 Aug 2019 - 9:05, https://dozenal.forumotion.com/t3-dozenalizing-metric wrote:In my dozenal C.O.F. system, i divide the day into 12 hours of 144 minutes, or 144 seconds, but this second is still too long.  Luckily an instant of 1/12 second works wonders.

In the Pendulum system, while the magnitude of the density of water is one unit, the unit of length may be small in comparison to time for the purpose of derivation of units. There may be merit therefore in discussing a larger unit of length such as the decimetre and how to justify this unit dozenally. What appears to be a prevailing view of a system based on a decimetre has been conveyed.

wendy.krieger on Fri 20 Sep 2019, https://dozenal.forumotion.com/t22-the-design-of-the-c-o-f-system#94 wrote:Given that the usual practice is to select base units from the acts of legislation, it is highly unlikely that an instant be included in this, given that most people don't need it.  So the most probable system of units from COF, would be the dm.kg.s (units of 10, 1000, 10 COF, dozenally).

The Pendulum system where the basic unit of length is the centimetre is preferred because of its dozenal justification through the pendulum and its presence in historical and ongoing units such as the mole. Nevertheless, a system based on the decimetre would be given attention if it could be derived in a dozenal fashion.

Phaethon wrote:In the Pendulum system, the basic unit of time was less than a conventional second, but the hectosecond is proposed for ease of convertion from metric units, and this caused powers of the units of the Pendulum system to result. It is claimed that there is a difficulty in part due to the basic unit of time, while it may be transiently brief by human understanding, being too long because of the powers it produces.

In recent minettes, I have thought of a possible solution to these large or small powers, which is to use as the basic unit of time a period of 25/432 seconds, a twelfth of the previous (5/6)^2 seconds basic unit of time. Then, instead of a hectosecond being a square dozen of time units, it would be a cubic dozen of the smaller basic unit of time. Twelve times this smaller basic unit of time could be used as the same period of the pendulum as before for the derivation of the other units.

Phaethon wrote:ten cubic decimetres

This is too obviously wrong and the post is too old for this to require correction. Ten cubic decimetres would be ten litres, far larger than a centilitre. Clearly, the intention was ten cubic centimetres. The cubic centimetre as a millilitre is a very familiar unit of volume in grocery items. The notation of a cubic centimetre is used in preference to that of a millilitre in science. The decimetre is not generally encountered and litres do not tend to be notated as cubic decimetres.