The French could have simplified measuring systems by using 39.6 inches as a metre but for various reasons they ended up with 39.37. So a scaled down version was used.

So to dozenalise the metre a scaled down version of the imperial inch is needed.

100 / 39.37 = 2.54000508

2.54000508 x 39.37/39.60 = 2.525252525252525 recurring centimetres.

This is 2.5 x 100/99 for a reason.

The imperial is base 99 the metric is - well you all know.

Using this 'metric inch' the metric system becomes an exact scaled down replica of the dozenal imperial system.

We don't actually need a dozenalised metre or a redefined inch ...

We need a dozenal metrological system that will replace both the present metric system and the present Imperial units. There are good proposals for such a system in other threads which are not based on units, actual or redefined, from the present metrologies or historical ones.

There are good proposals for other systems on other threads but this one is about the metric and imperial.

There are some very smart people on this website and some of the ideas they have come up with are brilliant.

Knowing that the imperial is base 99 and the metric is obviously base 100 then a unit of 2.5 x 100/99 to flick the switch from metric to imperial is worthy of consideration, i don't see that anyone has realised that the imperial is base 99. Also the length of the units is immaterial as the numbers within the systems are universal, the inch can be any length you want because it represnts number one in the dozenal system. In the base 100 system it is represented by 0.12 inches or 100th of a foot.

The imperial is also base 32 and this is computer speak as you know.

At a pinch it is base 128 as follows

5280 / 128 = 41.25 feet or 495 inches (base 99.)

You are saying we don't need the imperial system but you don't know that it is base 32 (320 rods in a mile) and base 99 (6 rods).

320 x 99 is 31680 and in metrological terms this is very significant because when converted to base 102 it becomes 32640 and this is the unit discovered by Professor Alexander Thom in the mid 20th century.

Just over two years ago I wrote a book called

'Cracking the Megalithic Code' 'Stonehenge, It's about Time'

It suggests the ancients used the imperial system and one mile represents one day in time. the unit 3.666r feet was key as it represented one minute.

31680 feet is 6 miles and this presents the idea better as it is possible to drill down to the unit that represents the second.

31680 / 24 = 1320 (this is 10 x 11 x 12)
1320 / 60 = 22 (the numerator of Pi and the chain in yards)
22/60 = 0.36666r (or 11/30 and the unit is the ancient barleycorn one anglo saxon inch divided by 3)

In the system Thom discovered the unit changes to 3.7777r.

the difference between the two units is 0.1111r and dividing this into each unit gives 33 for the imperial and 34 for Thom's system.

So all i am saying is don't be too hasty to write off the imperial system especially as the metriic system imperialised has the polar circumference as the unit reference point. The French made it so, much to their credit.

It is difficult to get a reference point for any base unit in any system but the Earth circumference is hard to beat.

You may find, after all, that the imperial system is actually what you are looking for as it represents bases 1-12 and multiples of these numbers such as 9 x 11.

Shaun @ Aug 20 2017, 03:22 PM wrote: We don't actually need a dozenalised metre or a redefined inch ...

We need a dozenal metrological system that will replace both the present metric system and the present Imperial units. There are good proposals for such a system in other threads which are not based on units, actual or redefined, from the present metrologies or historical ones.

The metric system is here to stay forever. On October 20, the International Committee for Weights and Measures (CIPM) submitted a resolution recommending the use of the new values and the redefinition of the SI to the General Conference on Weights and Measures (CGPM), the official body that makes changes to the SI. In November 2018, the CGPM will formally vote on the adoption of the revised system. The CGPM includes members from dozens of nations, including the U.S. and other signatories of the Convention of the Meter, the 1875 treaty that standardized measurement units on the international level.

The new values referenced here are the fixed definitions for the Boltzmann constant, the Planck constant, Avogadro's number and the charge of the electron. Based on the latest research, these values will now be fixed values, meaning that all of the SI units will now be fully defined from invariable constants in nature. It is the first time in history that all the base units of this wonderful system will be defined from invariable natural constants.

“It’s a broader philosophical paradigm shift,” Mohr said. “When the speed of light became a fixed number, researchers stopped measuring the speed of light. They focused on realizing the meter. It’s the same with the Planck constant. You’re not going to be measuring the Planck constant anymore. You’re going to be realizing mass and electrical standards more precisely.”

A lot of time and money went into the research to bring us to this point. It has the support of the whole world, especially the people that matter in the fields of science and engineering. You're wasting your time dreaming of a dozenal measuring system. Best to adopt SI with dozenal devised prefixes.

2019-0-20, international metrology day, honouring the day in 1875 that the treaty of the metre was signed will be a very important day in the history of the world.

davidk @ Aug 23 2017, 04:43 PM wrote: There are good proposals for other systems on other threads but this one is about the metric and imperial.

There are some very smart people on this website and some of the ideas they have come up with are brilliant.

Knowing that the imperial is base 99 and the metric is obviously base 100 then a unit of 2.5 x 100/99 to flick the switch from metric to imperial is worthy of consideration, i don't see that anyone has realised that the imperial is base 99. Also the length of the units is immaterial as the numbers within the systems are universal, the inch can be any length you want because it represnts number one in the dozenal system. In the base 100 system it is represented by 0.12 inches or 100th of a foot.

Are you still pandering this idiocy? Nobody cares or will be convinced. Now that the SI will be redefined so that all of the base units are defined from fixed values of natural constants, all of your gibberish is moot.

What Harold mentions is pretty much the problem I have actually trying to use any of the proposed dozenal systems: I may love the ideas, especially for Primel, but realistically, unless there are exact metric equivalents, I can't use them in real life, because all my measuring devices are in SI.

There are unfortunately two problems. The first problem is that "kilogram" already has a prefix, despite being a base unit, and applying a dozenal prefix on top of that to give constructs like "unciakilogram" starts to sound ridiculous. But we could resurrect the original French name "grave" for the kilogram to resolve this.

The second problem is that despite all the redefinitions, the units have to retain backward compatibility with the old definitions and be very, very close to them each time, all the way back to the French National Convention of 1793 for the metre and kilogram, where the gram was defined as the weight of a cubic centimetre of water. So even today with the redefinitions, the density of water is still very close to 1 g/cm^{3}. If you use the kilogram as a base unit, these powers of ten put a component into the system that is inextricably decimal.

Because of this, it seems that we have only two palatable choices for a dozenalised SI: either we just ignore this and let the density of water be 6b4 kg/m^{3}, removing a nice round number (but then the densities of most substances aren't exactly nice either), or we use the centimetre and gram as base units instead of the metre and kilogram.

The best basis of the metric system, to use to dozenalise etc, is not the metre-kg-s base, but the dm-kg-L base. This can be coupled effectively to dozenal time.

The unit names in metric are not themselves suited but the LinnBase system gives alternate names for these.

The Linn or decimetre, 20736 gives a "mile", but with the hour as 2 metric units, the speed unit is 1.0368 km/s, which means that you can convert numbers directly. Also, many of the numbers we need give caution to, like bridge clearences etc, are in decimetres already.

Heights in centimetres are then converted at the tens, so 185 cm becomes 166 decilinn, since 18.5 = 16;6.

The Arr and Soll are square and cubic Linns, a measure of 1,0000z Arr is about 2.0 ares, an acre is some 18z Arr-measures.

The Capp is a replacement litre, but since the normal cup is 1/4 capp, and the teaspoon is 1/48 cup, we get a teaspoon as 9 millicapps, the cup at 30 centicapps, &c. Lots of things are sold by the litre.

Weights are based on the Pondd, but the name i used 'chog' is basically a prefix-free unit that is neither gram nor pound. You can still have pounds as 600 millichogs, and divide this. The chinese picul is the weight one might carry on a beam, divides into 100 catties. If one supposes something like dec 60 kg for the picul, the catty is 600 grams, and the mace as 37.5 grams. Revised, one would need to preserve the 100; relation giving a picul at eg 46 chogs, the catty at 460 grams and the mace at 46 grains, exactly 1/14; of the european pound (ie an oz).

It is not really something one would do as a system, but to create a source of dozenal figures for the mind to much on.

Twelfty is 120 dec, as 12 decades. V is teen, the '10' digit, E is elef, the '11' digit. A place is occupied by two staves (digits).
Digits group into 2's and 4's, and . , are comma points, : is the radix.
Numbers writen with a single point, in twelfty, like 5.3, means 5 dozen and 3. It is common to push 63 into 5.3 and viki verka.
Exponents (in dec): E = 10^x, Dx=12^x, H=120^x, regardless of base the numbers are in.

For those of us who are agreed that we want dozenal instead of decimal:

Neither our Imperial units nor the decimal metric units are suitable for use with dozenal notation. We need a system rationalised for dozenal counting.

This calls for a dozenal metrological system to replace both the present metric system and the present Imperial units, not something based on units, actual or redefined, from the present metrologies or historical ones.

Whether or not you believe the dozenal system will eventually replace the decimal system does not affect the fact that the dozenal system requires its own metrological units.

I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.

I agree with this, theoretically, but trying to work with Primel with SI equipment is a rather futile exercise in conversion, because I don't exactly have the means of getting Primel equipment, even a basic ruler or weighing scale.

I wonder: if the Dozenal Societies could come up with some basic Primel or TGM measuring devices (rulers, thermometers, weighing scales, measuring cups...) to sell, we might be able to actually use these new units practically.

I don't think forcing a new system in by dictating is a plausible thing, let alone a good thing. What we need to do, IMHO, is to expose more people to the idea that dozenal is possible as an alternative to decimal, and that it has good arguments in its favour based on solid mathematics, and give the possibility to try to use it for themselves. I don't think we can ever have dozenal triumphant over decimal, but having it as an alternative seems to be doable.

Double sharp @ Oct 29 2017, 03:44 PM wrote:I wonder: if the Dozenal Societies could come up with some basic Primel or TGM measuring devices (rulers, thermometers, weighing scales, measuring cups...) to sell, we might be able to actually use these new units practically.

I don't think forcing a new system in by dictating is a plausible thing, let alone a good thing. What we need to do, IMHO, is to expose more people to the idea that dozenal is possible as an alternative to decimal, and that it has good arguments in its favour based on solid mathematics, and give the possibility to try to use it for themselves. I don't think we can ever have dozenal triumphant over decimal, but having it as an alternative seems to be doable.

Tom Pendlebury produced a set of weights and measures (the picture of him shows him at a stand with all on display) but I don't know what happened to them when he died; they certainly never reached me when I resumed the helm after Arthur Whillock died (maybe he never got them from Don Hammond). If I had the skill I would make ny own, but regret arthritis somewhat impedes my abilities nowadays. You could of course try making your own for your own use to see how well they may work for you.

My point was simply that for any number base to be of use as the norm (be that dozenal, base sixteen or whatever) then the associated metrological system for that base shold have all its units (length, weight, time etc) specifically created to fit that base.

I mean, there’s a CNC mill and lathe at my university, as well as a couple injection moulding machines. I could potentially manufacture a Primel ruler, a set of weights and a set of measuring spoons, but I don’t have the material for it.

Shaun, I didn't mean to suggest that you approve of dictating measures at all, and only raised it as a bad possibility: I can see how it could have been taken that way and apologise. The fact that we don't want to do it is why I think Harold's concern doesn't quite apply: we're not here to replace SI, which works perfectly well for decimal, but to provide the opportunity for dozenal immersion and let people judge for themselves and actually try out base twelve. So something like Primel or TGM works perfectly well here.

Even the multiple possibilities for each unit name in Primel are a demonstration of the principle of providing alternatives. I am rather too immersed in metric culture to really remember all the colloquial names of the units, especially with not much active use, and tend to just say "unciaday, biciaday, triciaday, quadciaday, pentciaday, hexciaday"; but no doubt many others would prefer the more vividly evocative names.

(This is why, incidentally, I have not constructed the octal and tetradecimal Primel-like systems I remember I have mentioned before: the issue of coming up with the colloquialisms, which for myself is rather difficult! But maybe I could just give a list of the units with metric and some USC equivalents and leave it to you or Kode to suggest them.)

Double sharp @ Oct 29 2017, 03:22 AM wrote: What Harold mentions is pretty much the problem I have actually trying to use any of the proposed dozenal systems: I may love the ideas, especially for Primel, but realistically, unless there are exact metric equivalents, I can't use them in real life, because all my measuring devices are in SI.

There are unfortunately two problems. The first problem is that "kilogram" already has a prefix, despite being a base unit, and applying a dozenal prefix on top of that to give constructs like "unciakilogram" starts to sound ridiculous. But we could resurrect the original French name "grave" for the kilogram to resolve this.

This has been brought to the attention of the BIPM over the years, but they don't seem to think it is a big enough issue to rename the kilogram. If the day should come where it becomes an issue, i'm sure they would rename it.

The second problem is that despite all the redefinitions, the units have to retain backward compatibility with the old definitions and be very, very close to them each time, all the way back to the French National Convention of 1793 for the metre and kilogram, where the gram was defined as the weight of a cubic centimetre of water. So even today with the redefinitions, the density of water is still very close to 1 g/cm^{3}. If you use the kilogram as a base unit, these powers of ten put a component into the system that is inextricably decimal.

All of the redefinitions have been fully backwards compatible. All that redefinitions do is decrease the uncertainties and increase the repeatability. The only unit I'm aware of that will actually have a noticeable difference under the new changes, but only to scientists, is the volt. The precision of your voltmeter is such it won't notice the difference.

Because of this, it seems that we have only two palatable choices for a dozenalised SI: either we just ignore this and let the density of water be 6b4 kg/m^{3}, removing a nice round number (but then the densities of most substances aren't exactly nice either), or we use the centimetre and gram as base units instead of the metre and kilogram.

Making all of the physical constants exact values in SI makes all of constants highly inexact in other systems. The values have never ending decimal values that lose accuracy no matter where the number is truncated.

With the whole world SI and everything traceable to the BIPM, I can't see any other system taking root. There would have to be a dozenal equivalent of the BIPM to organise and maintain the units and definitions. The only thing sustaining the life of imperial and its clones is its attachment to SI units, even though the definitions are impracticable.

In the sense that the IEC has created binary multiple prefixes for use with the bit and byte, technically, they can be used with any other SI base unit. Thus there is no reason why dozenal prefixes also can't be created.

wendy.krieger @ Oct 29 2017, 11:30 AM wrote: The Linn or decimetre, 20736 gives a "mile", but with the hour as 2 metric units, the speed unit is 1.0368 km/s, which means that you can convert numbers directly. Also, many of the numbers we need give caution to, like bridge clearences etc, are in decimetres already.

The unit names in metric are not themselves suited but the LinnBase system gives alternate names for these.

Heights in centimetres are then converted at the tens, so 185 cm becomes 166 decilinn, since 18.5 = 16;6.

The Arr and Soll are square and cubic Linns, a measure of 1,0000z Arr is about 2.0 ares, an acre is some 18z Arr-measures.

The Capp is a replacement litre, but since the normal cup is 1/4 capp, and the teaspoon is 1/48 cup, we get a teaspoon as 9 millicapps, the cup at 30 centicapps, &c. Lots of things are sold by the litre.

Weights are based on the Pondd, but the name i used 'chog' is basically a prefix-free unit that is neither gram nor pound. You can still have pounds as 600 millichogs, and divide this. The chinese picul is the weight one might carry on a beam, divides into 100 catties. If one supposes something like dec 60 kg for the picul, the catty is 600 grams, and the mace as 37.5 grams. Revised, one would need to preserve the 100; relation giving a picul at eg 46 chogs, the catty at 460 grams and the mace at 46 grains, exactly 1/14; of the european pound (ie an oz).

It is not really something one would do as a system, but to create a source of dozenal figures for the mind to much on.

The best basis of the metric system, to use to dozenalise etc, is not the metre-kg-s base, but the dm-kg-L base. This can be coupled effectively to dozenal time.

Says who? The present base system suits those units greater and less than the base. Pleasing the whims of one side puts the other side at a disadvantage. Plus the SI base units are already accepted and standarised world-wide. That isn't ever going to change.

Shaun @ Oct 29 2017, 01:54 PM wrote: For those of us who are agreed that we want dozenal instead of decimal:

Neither our Imperial units nor the decimal metric units are suitable for use with dozenal notation. We need a system rationalised for dozenal counting.

This calls for a dozenal metrological system to replace both the present metric system and the present Imperial units, not something based on units, actual or redefined, from the present metrologies or historical ones.

Whether or not you believe the dozenal system will eventually replace the decimal system does not affect the fact that the dozenal system requires its own metrological units.

Who says the decimal metric base units are not suitable for use with dozenal. Care to offer proof of some type?

Yo realise that any new system not tied in some way to SI has a zero chance of adoption? I mean dead zero. With all of the metric base units being perfectly defines, that cements their continued existence as long as there is a BIPM. There is no reason for there ever not to be. The only thing that can possibly cause a reboot is if society is nuked back to the pre-stone age and that assumes the survivors already familiar with base 10 will take the effort to change bases.

Harold @ Nov 5 2017, 12:31 PM wrote: Yo realise that any new system not tied in some way to SI has a zero chance of adoption? I mean dead zero. With all of the metric base units being perfectly defines, that cements their continued existence as long as there is a BIPM. There is no reason for there ever not to be. The only thing that can possibly cause a reboot is if society is nuked back to the pre-stone age and that assumes the survivors already familiar with base 10 will take the effort to change bases.

Oh I very much agree that there is zero prospect for dozenal being triumphant over decimal. But we can make people think about various bases, see the mathematical properties of them, and perhaps question why is it we are decimal, and maybe see how things would be like in another base. That, I think, is why the DSA website says "Why do some people propose that we learn to count in twelves in addition to counting by tens?", with the words "in addition to" and not "instead of".

icarus @ Nov 5 2017, 03:55 PM wrote: Harold sounds like a troll.

Sounds very much like a couple of our past trolls. Not so much interested in discussing dozenal as simply telling us we're wasting our time to do so.

Somehow telling a metric system enthusiast that the metric system is not perfect seems to hit a raw nerve.

Harold is repeating the same mantra over and again. If he continues to do so then I see no reason why he should not be asked to go and irritate someone else.

icarus @ Nov 5 2017, 03:55 PM wrote: Harold sounds like a troll. The premise here is not "it is useless to resist us," but free thought.

If I get three people seconding the motion, I'll deem Harry a troll and send him to pasture. Otherwise he's free to be our pet contrarian.

I do not think Harold is a troll, or at least I do not think he is one based on the behaviour he has shown so far in this thread. He certainly has strongly worded opinions, but he doesn't seem to be against the idea of dozenal, since he has suggested a dozenal BIPM and dozenal prefixes for SI units. We may not agree that this is ideal, but it certainly furthers the idea of dozenalism, and he is not just being contrarian against dozenal in toto.

But I will of course bow to consensus, since his general intransigence is not easy to deal with, even though it is also somewhat well-founded.

The point being made is that if you use a unit of 2.5 centimeteres and multiply it by 100/99 this gives 2.52525252r centimeteres x 39.60 gives one metre,

1.3333r metres then represents 52.80 units and the metric system becomes the imperial without changing the length of the metre.

This must surely confuse Harold because he does not seem to be able to see this.

22.66666666r metres becomes 897.6.

897.6 x 12 = 10771.20 x 2.525252525 = 27200 This is an ancient unit of measure discovered by Alexander Thom.

To change decimal to imperial convert using 100/99 this is 1.0101010101010r.

Converting the polar circumference gives 40000000 x 39.60 = 1584000000

divide by 12 gives 132000000

by 5280 gives 25000. The same circumference but in imperial notation ( not the imperial system a decimalised/dozenalised version of it)

davidk @ Nov 6 2017, 05:56 PM wrote: 1.3333r metres then represents 52.80 units and the metric system becomes the imperial without changing the length of the metre.

This is not the Imperial system. It’s off by a factor of 1.00584, which may not seem significant, but it’s beyond the tolerance of most manufacturing processes.