## Metric II

## Metric II

(OP)

The original post is getting a little hoary -- not to mention hard to read.

So this is an opportunity to continue the debate in a nice, new post where people may actually read your input because they don't have to wade through 100's of other posts to do so.

So this is an opportunity to continue the debate in a nice, new post where people may actually read your input because they don't have to wade through 100's of other posts to do so.

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

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James Goodstadt

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ChemE, M.E. EIT

"The only constant in life is change." -Bruce Lee

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Go Mechanical Engineering

Tobalcane

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When we weight something in metric we weight according to Isaac Newton's Second Law of Motion. The acceleration of an object is proportional to the force exerted on it divided by the mass. This is how force is normally defined, by the formula usually stated as F = k·m·a. (The units can be chosen so that k = 1 and the formula then becomes F = m·a in that system of units.) So force is measured in Newtons, while mass is measured in Kilograms.

Gravitational force (one kind of weight) is what makes it difficult to lift objects up, and mass is what makes it difficult to move objects sideways (complicated by friction).

If we think further, then a balance measures mass and not force. However, the spring scales and load cells measure force (Robert Hooke expressed his Law that the distance a spring stretches is proportional to the force exerted on it).

The magnitudes of the measurements of mass and force (weight here) may be the same, within the limits of the precision of the measurement, at some places on earth if the mass is measured in pounds mass and the force is measured in pounds force, for example. But the magnitudes are never the same on Earth if the mass is in kilograms and the force in newtons, or the mass in pounds and the force in poundals!

The pound mass is the older definition of the pound. It is also the primary definition of the pound. Before the redefinition of the pounds as fractions of a kilogram, they were defined as the mass of independently maintained artifacts. 1 pound avoirdupois as 0.453 592 37 kg (US).

The modern practice is to use pounds for the mass units. If the force units of the same name are used, they should be identified as such (pounds force).

GSC

## RE: Metric II

In addition, my son has just started work with a refrigeration company and he comes home telling me that 'today Dad, I installed a 3 ton AC unit using 3/8 pipe and the brackets were 3 feet wide. The refrigerant gas fill was 200 grammes and the plantroom he put the AC plant in was 30 feet in the air and measured about 20 feet by 5metres. He also tested the system to something like 250PSI.

I Give up.

What is the world coming to.

Someone help me before I go mad.

Friar Tuck of Sherwood

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Because a system that requires three orders of magnitude between unit increments is not practical.

Hg

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Most of the formulas I use are imperial, and most of my design is done in imperial units. Having said that, all of the work I produce is released in metric.

The set of plans I design in imperial, convert to metric is then converted back to imperial by the various contractors and suppliers that use the plans. We actually release a table in our specifications that states what we mean when we say 300mm x 300mm duct.

It makes me laugh... but maybe my daughter (who is only one) will one day get to work only in one set of units.

**If you are not part of the solution, then you are part of the precipitate.**

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We have converted all the instrumentation into oilfield units, the only concern that we have is that a Norwegian driller, when told that the mud is 10.4 pounds per gallon in, but 9.8 pounds per gallon out, won't know instantly that that is BAD, as he'll still be working out in his head "9.8ppg that's equal to let me see...about 1.18. 1.18!!! oh Shiiii...."

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I have read nearly all these posts and have noticed many pros and cons for both metric and Imperial/Customary systems of measures. It would seem to me that neither system is ideal in all situations and for a number a reasons. The Imperial system (and its many similar European counterparts) used multiple named units based roughly on either body parts or what were items of common knowledge such as grains. The obvious disadvantage was the complete irregularilty of the different magnitudes (e.g. 12 inches in a foot, 16 ounces in pound, 1760 yards in a mile and so on. This of course made for extreme difficulty in computation of multiples and subdivisions and an even bigger problem in working with compound units.

The advantages of most of these units was the relevance to day to day usage, and their basis in the case of length to body parts and the relative ease of remembering and recording values of usually one or two digits with only infrequent forays into three digit values or more. Another great advantage of many of these units was their exact divisibility into halves, quarters and significantly, thirds.

The French scientific establishment attempted to bring order to this chaos and introduce the metric system. A brilliant idea, but grossly flawed in its choice of number base. Although the Hindu-Arabic number system had been in use in Europe to differining degrees for about 600 hundred years, it did not come into general use until about the 16th century and then of course only by the educated and merchant classes. When did universal education begin in Europe and so when did literacy and numeracy become widespreaed? Thus, had the French used a base 12 number system at the time Napoleon introduced the metric system it would not have been a major task. As it was, the system was opposed by the French populace, was then rescinded and only reintroduced in the 1820s when it was also introduced in the school system.

So, if we had a system of weights and measures based on a duodecimal number system, we would have all the advantages of the current metric system plus the added advantages of simpler calculation. Not only that but the system could still retain its scientifically based suffixes for engineering and scientific uses, but could also retain many of the familiar common unit names for day to day commerce. In fact, even with the metric system today, there is a growing trend to assign common names to many metric measures. In the early 1900s Germany redefined the pound (Pfund) to be exactly 500 grams and Germans today still order cheese and cut meats by the "Pfund" or "halb Pfund". Metric glasses of beer in Holland are ordered in "Pintjas". I am sure there are many more examples and would welcome contributions to the list.

So, to summerize, lets have a worldwide metric system but lets make it a duodecimal one.

All that is needed to bring it about is for American industry to find a significant economic advantage it may give over their competitors and it would be on its way.

PS There is nothing special about base 10. In base 12, (in which 12 decimal is written as 10), multiplication and division by 12 (10) would work exactly the same, add a zero or move the point one place left correspondingly. Oh and of cours, 1/2 would be 0.6, 1/4 would be 0.3 and 1/3 would be 0.4, exactly!!!

PPS. Note that in the world in which we live, our three dimensional space is better suited to packasging items in dozens. Twelve items can be packed as 1 x 12, 2 x 6, 3 x 4 and even 2 x 2 x 3. Ten can only be packed 1 x 10 or 2 x 5. As a result of this, during the second world war a\group of clerks in the Army Transport Service found the erconomies of using duodecimal arithmetic so great in figring cubages of packing cases for goods to be sent to war after reading an article by an Amercan, F. Emerson Andrews.

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I think there would definitely be an economical advantage for companies to switch to metric (base 10), maybe even a bigger advantage than when every country switched to one single currency.

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Where did I say the French invented base 10? All I said was that they made the mistake of using base 10 when they introduced the metric system. They could just as easily taken a harder look at the decimal system and extended it to a duodecimal system with the addition of two more symbols and from there developed the metric system based on that number base. Note that the name metric does NOT imply a decimal base as the Greek word from which it derives means roughly "to measure".

As for the Romans, they did not use a true decimal system as they had symbols for 1 and 5 and all their multiples, that is for integers. For fractions, the Romans used a system of names for fractions in TWELFTHS and many submultiples of these. Why, because it makes more sense to be able to work in a system that allows for exact halves, qaurters AND thirds, something our decimal system does not do nor most other bases suggested as alternatives (binary, octal or hexadecimal.

If using a system of weights and measures that had the most often used measures subdivided into 12ths was so bad, why did it last for so long? History should tell you that if something does not suit the uses for which it is intended, it will tend to fall out of use. But the old 12 base stayed with us in our lengths and weights for hundreds if not one or two thousands of years despite the use of a decimal based number system, and of course are still here today in clocks and compasses.

Note that I am not saying such a system would be easy to implement, but rather it would be a better system.

As for the ease of switching from base 10 to base 12, what is your justification for saying it would be like changing to driving "upside down". Have you done any pilot studies? Have you performed a case study? Have you collected any evidence to support this assertion?

Apart from that, I think you are being very dismissive of people's abilities to effect such a change. After all, the British switched from a system of 12 pennies to the shilling, 20 shillings to the pound (all done while using a decimal number system) to a pure decimal system. And if I'm not mistaken, one nation was able to send men to the moon and bring them back again using systems developed under the US Customary system of measures (with the help I suppose of one or two engineers). I don't think you give people enough credit.

Furthermore, if as was done by the French under Napoleon the system was taught in schools, then in one generation you would have a duodecimally cognizant population. It is only we who have been taught one system that would have difficulty in "unlearning" our decimal times table. As for changing existing systems throughout the world, we now have a positive advantage to assist in that process, something called I think "computers".

Penultimatley, your thought that there would be an "economical advantage for companies to switch to metric (base 10)" would be better than a multitude of different systems is not in question, but that does not invalidate the argument that the use of a base twelve system of numbering and a coherent system of weights and measures based on that number system would be even better than the base 10 system, now erroneously called the metric system. Any number base could be used and still be called a "metric" system.

To conclude, making comments on your beliefs in the suitability of one system versus another is perfectly valid, but they are just that, your unsubstantiated beliefs. When you have completed a full investigation of the pros and cons of different number bases I would be happy to hear your results. And if you are about to ask have I done such a study then the answer is "YES". It would still be a valuable input to see the results of similar investigations by others if they care to provide them as it would serve to point out any flaws, false assumptions or erroneous conclusions in my own work.

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Are you advocating shifting to an entirely base-12 number system? "10" would mean twelve, etc.?

Or a system in which each prefix level means 12 of the previous? So 1 dam would be 12 m, and 1 dm would be 1/12 m?

Surely you aren't advocating changing the entire number system, or implying that failure to do so was merely a Napoleonic oversight. That system had been in place by then for the better part of a millenium. Choice of number system is hardly on the same level as the relatively trivial matter of which units to use to label said numbers.

But that only leaves the possibility that what you're advocating is the mess of combining a duodecimal unit system with a decimal number system. The whole point of the "metric" system was to have a system of units that were easy to relate to each other--you convert one to another simply by moving the decimal place around.

I must be missing something.

Hg

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*LOL*

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Apologies for my inadequate explanation but to describe the proposal in a short post is perhaps unfair to readers. However I shall try to end your frustration.

"Are you advocating shifting to an entirely base-12 number system? "10" would mean twelve, etc.?"

Yes I am. There is nothing strange about this. *I'm sure you have had experience of hexadecimal numbering where letters A to F are used to represent values 10 to 15 decimal and 16 decimal is represented as 10, meaning one group of 16 plus zero units. In this system 20 would be decimal 32 and so on. 100 in hexadecimal is 16 x 16 decimal or 256.

In a base 12 system of course 10 would be 12 decimal, 20 would be 24 decimal and 100 would be 144 12 x 12 or 144 decimal.

In each of these positional notation systems each succesive position is the next succesive power of the base. Because base 10 has only 10 digit symbols (0 - 9). A base 12 system would require two new digit symbols to represent values of 10 and 11 decimal.

OK, so having defined the digits and retained both the positional notation of the decimal sytem, what does base 12 do for us? Well to begin, multiplication by 12 in this system would work exactly the same as multiplication by 10 in base 10, you just add zero. Likewise, dividing by 12 (written as 10 in base 12) just means moving the point one position to the left. This functionality is the same for all base systems, multiply or divide by the base and you just move the point right or left.

Ok, so why bother when we already have that in our decimal system. Well that comes back to the question of why people continued to use twelves for millenia despite using a deciaml number system. Why, because it was very useful. You can take a half of 12 (6) or a quarter of 12 (3), but even better you can take a third of 12 (4) without any fractional parts or repeating digits. So in base 12, 1/2 = 0.6, 1/4 = 0.3 and 1/3 = 0.4. This is just one simple example of the advantages of base 12.

Now, if we assume the implementation of a base 12 number system, then all weights and measures should also use the same system. Thus the basic measure for length would be subdivided into 12 parts, and each of these subdivided in 12 parts and so on. Likewise multiples of each measure would be 12 times the preceding value. Of course, these would all be written as 1, 10, 100, 1000 ... and fractional values 0.1, 0.01, 0.001 ...

Now about the "Napoleonic oversight", it was one of the progenitors of the metric system that in retrospect made a comment that in hindsight that the system would have been better based on 12. Yes the decimal system was in use for hundreds of years and is believed to have ecolved because we as humans have two hands with five digits each. But I think we have all gone beyond the stage of counting on our fingers.

Finally, your question of whether I am advocating the combination of a decimal and duodecimal system is not what I am suggesting. I am saying leave the decimal system behind and use a pure duodecimal system throughout.

If my explanation still leaves you confused then that is possibly a deficiency in my presentation. You can however find many excellent references to various number systems including duodecimal on the web.

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I,m not saying the old measures weren't good, just that they can be improved beyond what even the metric system provides.

A set of measures with a consistent increase in magnitude (as in the metric system) but with advantages not found in the decimal based metric system. Division by 2, 4 and 3 without irrational numbers as results in the case of division by three, statement of values with fewer digits than the decimal system both for integers and fractional values, greater regularity in the multiplication table, and significant improvements in visual identification of factors and divisibility.

Further benefits include finer graduations in fractional values and the retention of easily recognized names for commonly used measures, and the consequent ability to specify measurements using single or double digits for most commonly required day to day usage.

PS As an example, not necessarily part of the proposed system but what we should expect, I quote an adverstisement from my local chemist (Drug Store for our cousins across the pond) for photo prints from digital media.

151 x 102mm (6" x 4")

photos price each

1 - 19 49p

20 - 49 39p

50 or more 29p

203 x 151mm (8" x 6")

photos price each

1 - 19 £1.19

20 - 49 99p

50 or more 79p

I know which form of measures I prefer to quote (and remember). I dread the day when the Imperial measures are removed entirely.

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Of course a duodecimal system already exists in that we have the dozen as a recognized measure of quantity. Though I did here of one tale of MacDonalds selling chicken wings in portions of 6, or 12. When the person asked for half a dozen they were told, "sorry sir we only sell them in portions of 6, or 12" ... You just can't win

corus

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You have ignored totally the items you can't refute, in particular that 1/3 would be 0.4 exactly. Unless you are prepared to look at ALL of the advantages, citing a single item as a counterargument is just ducking the question of which system is better.

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- quite an interesting thread, I think.

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Steve Braune

Tank Industry Consultants

www.tankindustry.com

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That's not nearly enough to generate much enthusiasm on my part, particularly with the drawback that, as you said, we need two more digits to represents the numbers 10 and 11 of base 10 in a base 12 system. Plus, just about every measuring device currently in use from speedometers to pressure gauges to bathroom scales reports to us in a base 10 system. So, switching to a base 12 system would not be simply a matter of educating the next generation in school to use base 12 instead of base 10, we'd have the substantial expense of replacing an incredible amount of hardware and signage around the world that would become "wrong" since reading the speed limit sign that says 55 miles per hour would become 65 miles per hour.

Considering that computers and calculators can calculate 1/3 with enough digits to be precise enough for most work (certainly more so than any Roman base 12 scale, I'd wager) I just don't see how switching to base 12 can pay off.

Edward L. Klein

Pipe Stress Engineer

Houston, Texas

"All the world is a Spring"

All opinions expressed here are my own and not my company's.

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Sorry I couldn't include all the reasons in a post like this, as there are just so many. All I can do it state some of the advantages without providing the detailed tables and examples. I would be happy to provide much more by email if you wish, but for now will jsut stick to statements (which you could verify yourself by a little calculation).

1. Greater divisibility, since 12 has factors of 2, 3, 4 and 6, where 10 has only 2 and 5.

2. Reduction in the number of repeating fractions when expressed in duodecimal.

3. Simplified multiplication tables with more regularity in resulting values.

4. Visibly easier identification of divisibilty.

5. Representation of values with fewer digits.

6. As a result of 5, greater precision with the same number of digits, or equal precision with fewer digits.

7. Time is still predominantly based on 12, 2 x 12 hours per day, 5 x 12 minutes per hour and seconds per minute.

8. Measures of angles (apart from radians) is still predominantly 12 based with 3 x 12 x 10 degress in a full revolution.

As I said before, comparing tables of values in each number base would show the clear superiority of the duodecimal base for calculation. However, it would not be sufficient to introduce such a number base without also providing with it a coherent set of names, prefixes, and a consistent set of weights and measures.

The number base is just one part of a whole system. I may not have stated it before, but close examination of our current definition of the second and the metre from their original definitions onward shows clearly that the metre is a completely arbitrary measure resulting from circular arguments from the definition of the metre to the second, to to speed of light and back again to the metre.

"The senses imprison us, and we help them with metres as limitary,--with a pair of scales and a foot-rule and a clock." www.footrule.com

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What are the benefits of having say,

Π_{12}= 3.184809493...instead of the conventional 3.1415926535...? The same concerning other transcendental numbers like e, etc. ?What advantages would result from converting log

_{10}to log_{12}as, for example, when calculating pH ?While writing numbers in base 12 is one thing, would you orally still call 1300

_{12}(=2160_{10}) one thousand three hundred ? Wouldn't that be confusing and disruptive ?One comment:

At this stage, I must agree with the opponents to the switching over to base 12, in that given the inertia inherent in the use of the present decimal system, conversion would be far more trouble than its worth.

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If it was in base 12, we would require 2 new numerics for 10 and 11. Let's call them A and B for the sake of argument.

So then we have clockwise from the start - 1,2,3,4,5,6,7,8,9,A,B,10.

As opposed to:

1,2,3,4,5,6,7,8,9,10,11,12.

If we work in base 10, not base 12, then a duodecimal system is illogical. If we already had, and commonly used symbols for A and B, then base 12 would be the norm., and would make more sense.

Also,

But, what what about the inverse? 6/12 = 0.5, then 3/12 = 0.25 and 9/12 = 0.75. Other than that...

How about 10? 1/10 = 0.1, 2/10 = 0.2, 3/10 = 0.3 etc.

Since we currently already have base 10, introducing base 12 would be thoroughly confusing, as some would use 10 and some 12, so really you'd have to come up with symbols for 1 to 11 [base 10], or else you'd have to write 100

_{12}for 144_{10}. I have enough trouble with omission of units - i.e. pressure = 18, let alone thinking about which base it is in.## RE: Metric II

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TTFN

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Unc said, "All that is needed to bring it (a duodecimal system) about is for American industry to find a significant economic advantage it may give over their competitors and it would be on its way."

I can't see that happening. The idea, however, is kind of neat and I understand Unc's points. I hadn't thought of it before.

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Try to rearrange the atomic numbers of the periodic table of elements. U wouldn't be 92 anymore, but 78 !

Even the 55 mi/h limit would change to 47 mi/h !

All formulas based on log

_{10}would have to re-adapt, as for example, the Richter intensity scale of earthquakes.A Babel-type of confusion would be the result.

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If you really want to discuss base 12 as a substitute for denary then why not set up your own web site or discussion board to do so? Who knows, you may get so much traffic that you get rich beyond the dreams of avarice?

Base 12 is at the very least off topic for a forum entitled "Where is engineering going in the next 5 years", it would be more appropriate in a forum entitled "Engineering we do while off our heads on magic mushrooms". So far as I know there is no intention to start such a forum on eng-tips.

Cheers

Greg Locock