I have a relative who has worked for a timber importer and general timber merchants for about a year. Around six months ago, they decided to 'go metric' so far as all their sales were concerned.

He has recently started being retrained as a 'measurer' under the expert eye of the company's Senior Measurer.

Apparently, the key measure he is being taught to use is the 'bernicle' (at this stage I am not absolutely sure of the spelling).

Although my relative uses a calculator and checks his measurments by using it, he is (quite rightly of course) being taught how to calculate the area or volume (as the case may be) of timber in his head (just like a market trader would teach a youngster to reckon up a bill as he's in the process of bagging up items for a customer).

Apparently there is a real problem for timber measureres in reckoning up area or volume using either the centimetre (too short) or the metre (too long).

So they have inventied the 'bernicle'. And its length is, wait for it... 'thirty three and a third centimetres'.

This of course bears an uncanny resemblance to the foot!

They even use a 5-bernicle ruler, I understand.

I will post further details about the bernicle, its origins and use as I get them - but if anyone else can help, I'd be most grateful.

The story of the bernicle seems to encapsulate the whole argument between the easy-to-use, natural British/American system of weights and measures and the difficult-to-use, artificial metric system.

--------------------------------------------------------------------------------------------------------------

P.S. I understand that all the American timber still comes into the yard in Imperial sizes (widths), typically
1",
2",
2 1/2"
4", and
6".

As for continental timber, this comes in a series of curious sizes which don't appear to have any rhyme or reason to them. Again I'd be grateful if someone else (even xcole!) can explain them. The commonest widths for continental timber are, respectively:

26cm (sic)
50cm
63.5cm
80cm.

I would venture the suggestion that this is the continentals' close approximation to, respectively.
1",
2",
2 1/2", and
4".

There's absolutely no logic in them otherwise.

--------------------------------------------------------------------------------------------------------------

P.P.S. The news about the bernicle is not a wind-up, I promise you

Yes, in this country we call it *lumber*. It comes in standard lengths of 6', 8', 10', 12' (these lengths can be easily broken into halves, thirds and quarters) and in the common sizes and has traditionally always come this way when it is smooth milled. Years ago when lumber was sold only rough cut, it's actual size matched the nominal size, but if it's milled, these are the common sizes:

Nominal Actual
1x2 0.75"x1.5"
1x3 0.75"x2.5"
1x4 0.75"x3.5"
1x6 0.75"x5.5"
2x2 1.5"x1.5"
2x3 1.5"x2.5"
2x4 1.5"x3.5"
2x6 1.5"x5.5"
2x8 1.5"x7.25"
2x10 1.5"x9.25"
2x12 1.5"x11.25"
4x4 3.5"x3.5"
6x6 5.5"x5.5"
8x8 7.5"x7.5"
10x10 9.5"x8.5"

I have read that in metric countries, the wood comes in lengths of multiple 120 cm. (by the way Tony, you mean millimeters, not centimeters for your metric board sizes) I find that just a bit humorous because they're trying to use a dozenal system while confined to a decimal one. Why? Because the number 12 (and thus 120) can be divided not just 2 ways but it can be divided by 2,3,4, and 6. And in carpentry when things routinely must be divided into halves, thirds or quarters, lengths of base 10 will not work.
See
www.abc.net.au/rn/science/ockham/stories/s11563.htm
or http://www.tysknews.com/Depts/Metrication/metric_land.htm
for more on this.

Oh man,
ever heard of a cubic decimeter, also called liter ?
Thank you, I'll be here all the week.

Ralf

MattS: "You mean millimetres not centimetres..."

Quite so. I've simply no idea how I momentarily managed to confuse a centimetre with a millimetre - sorry about that

That damn "decimal point" eh?

Tcha!

It's rather that Tony doesn't know what he's talking about (the metric system).

Ralf

This is why the centimetre is never used in the UK construction industry.

All dimensions are given in millimeters.

Timber comes in sizes such as 50x100 or 50x150 or 50x200.

Plywood tends to come as 12.5mm thk or 25mm thk and a sheet of ply is 2400x1200.

Concrete slabs tend to specified as 100mm thk or 150mm or 200mm depending on the use.

Drainage pipes come as 100mm or 150mm or 300mm or 450mm.

And yes, I KNOW these are roughly equivalent to sizes in imperial. But if you loose the 0.4mm and standardise into multiples of 25 and 50 it suddenly becomes very straight forward.

Obviously Evil Engineer, you haven't checked the websites I posted for more reading on the subject, so I will summarize the arguments here.

Wood in metric countries comes in multiples of 2.4 cm not 2.5 cm. Why? Because 24 mm is more easily divisible than is 25. Furthermore, they call this unit a thumb...isn't that interesting? I find it amazing because another name for an inch is a thumb. Also, the boards come in lengths which are multiples of 120 cm. Why? Because you can divide 120 by 2,3,4, 5 and 6. Why? Because carpenters routinely divide things in halves, thirds, quarters and sixths. Remember, there is no such a thing as 1/3 meter.

Even so, you have another problem with your millimeter sizes. The numbers are HUGE! Metric measurements are in the form of four digit numbers. The four-part 'packages' are quite complex in that they don't have a reserved slot in a simple human mind. There are 10,000 possible four-digit numbers. So either the measurements have to be learnt by heart, a process which is slow and unreliable given the way an operation is continuously repeated throughout the day, or they have to be repeated over and over like a mantra while each measuring and cutting operation is performed, an equally unreliable process given the distraction factor during a construction process.

Even so, I suggest you go read these orations on problems related to the one's we're discussing.

http://www.abc.net.au/rn/science/ockham/stories/s11563.htm

http://www.tysknews.com/Depts/Metrication/metric_land.htm

I am now informed that the unit now called the 'bernicle' (33.33 ad nauseam cm) was invented several years ago by a timber merchant...er, because the timber measurers found metric units difficult to handle.

I will post more detail when I get it

Metric units aren't more difficult to handle than imperial ones. It's just a bit hard in the beginning to get used to it.

All things are difficult before they are easy.

Re: "Metric units aren't more difficult to handle than Imperial ones"

ANSWER: Where the numerical value of metric units is small, then of course they are no more difficult to handle than Imperial units e.g. 'How many square metres is a plot 5 x 8 metres?' is no more difficult than 'How many square yards is a plot 5 x 8 yards?'

One of the most serious problems about the metric system is the large numbers one is frequently expected to digest. Examples include:

* A jar weighing 730 grams (seen today at a farmer's market)

* A piece of furniture measuring 2230mm x 917mm x 293mm

* A distance sign giving a distance of 850 metres

[All the above are actual examples].

The joy of *all* customary systems of weights and measures i.e. 'natural' systems - instead of the artificial metric system - is that the they use small numbers which are:-
(a) easy to visualise, and
(b) easy to multiply (in your head)

>* A jar weighing 730 grams (seen today at a farmer's market)

What's difficult about 730 grams once you know that there are 1000 grams in a kilogram ?

>A distance sign giving a distance of 850 metres

What's difficult about 850 metres once you know that there are 1000 metres in a kilometre ?

>A piece of furniture measuring 2230mm x 917mm x 293mm

How would you write the above measurements in Imperial *without* reducing the accuracy by a factor of 25 ? (which is by rounding it up to the next inch)
2.54cm is quite a lot when it comes to figuring out if a piece of furniture fits into your room or not.

Ralf

Ralf wrote: "How would you write the above measurements in Imperial *without* reducing the accuracy by a factor of 25 ? (which is by rounding it up to the next inch) 2.54cm is quite a lot when it comes to figuring out if a piece of furniture fits into your room or not."

This is absolutely true indeed, Tony. Your comparison between metric and imperial is comparing apples and oranges.

Should apples by banned by those who prefer oranges?

Congratulations for totally missing the point, BWMA.

MattS said:
<<
Even so, you have another problem with your millimeter sizes. The numbers are HUGE! Metric measurements are in the form of four digit numbers. The four-part 'packages' are quite complex in that they don't have a reserved slot in a simple human mind
>>

This one gets rolled out quite a lot. And to be honest it's complete rubbish.

Is 475mm more difficult to remember than 1ft 6 and 11/16 ins ?

Personally, I don't think so.

If someone says "300 mill" or "890 mill" or whatever I can visualise it instantly.

Certainly more easily than I can visualise fractions in sixteenths.

It isn't "more difficult" or "less natural" it's just different.

Also fractions become irrelavent beyond 1/2, 1/3 and 1/4. Especially for the calculator generation.

Evil Engineer:

You know full well that those "metric" wood sizes are still "said" as 2by4 etc.

Guess why...

Obviously, since you think that fractions are irrelevant, you have never built anything yourself. I can't tell you how many times when doing construction that boards and other things must be split into quarters, thirds, halves, and so on. That's why boards come in lengths of things divisible by 2,3, and 4. Not only that, but you've never had to call out a measurement before if you think that metric sizes are easy to remember. The human memory works in packages. That's why telephone numbers are done in sets of 3 and 4 numbers. I can easily remember that a board must be 1' 6-11/16" Why? 1' is one package and 6-11/16" is another. So I measure 1' down and then over 6-11/16" You try calling out to a carpenter that he needs a board 1,234.37 mm and see if he can remember strings of numbers like that for multiple cuts.

You can't visualize 16ths? Next time you split a pizza or a pie you look how you would naturally split it into slices, and you tell me if you can do it quickly and easily into 10 equal slices. Half, quarter, eighth, sixteenth.

Visualization is the key to customary units. The whole human race knows what half looks like. I know what a gallon is, therefore I can instantly measure half a gallon. I know what an inch is, and therefore I can instantly see half of one.

<<
You can't visualize 16ths? Next time you split a pizza or a pie you look how you would naturally split it into slices, and you tell me if you can do it quickly and easily into 10 equal slices. Half, quarter, eighth, sixteenth.
>>

You are probably right provided that you do not split thing up too many times. At a certain point binary fractions becone very cumbersome - 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024 etc.

The fact of the matter is that for simple things, there is much to commend the imperial system. Once things stop being simple however, the imperial system becomes unweildy and the metric system comes into its own. This brings in the question as to where the boundary between simple and not-simple systems lie (or if it is necessary to have a boundary). In my view the minor inconveniences in simple matters are more than outwieghed by the simplicity of the metric system when analysing not-so-simple problems.

As far as splitting fractions is concerned, here are some conventions here in the US. Carpenters regularly work to the nearest 1/16" and that will suffice for framing a house. Sometimes the nearest 32nd is needed, but that is for very precise carpentry. Cabinet makers will work to such standards.

Very detailed engineering work will be expressed to the nearest 1/64th inch. Beyond the 1/64th division which is about the smallest that can be seen on a measuing device, the precision moves to what Americans call mils and the Brits call Thous, that is 0.001" and then down from there. I know, this sounds quite decimal; however, this is where your simple measurement problem becomes a "non-simple" one. There, it is quite legal to use the tenth hundredth and thousandth of an inch and beyond.

While that all may sound silly, and one may say, well you can use metric instead, that only works for your "non-simple" applications. For larger work, such as your carpentry, where things *must* be divided into halves, quarters, and thirds very often, the base 10 system breaks down. So why not use a system that has the capability to work duodecimally and decimally. I can measure things in tenths of inches or thirds, and you can't do that with a meter precisely.

>So I measure 1' down and then over 6-11/16" You try
>calling out to a carpenter that he needs a board
>1,234.37 mm and see if he can remember strings of
>numbers like that for multiple cuts.

As a side note, your comparison is unequal.
6-11/16" has an accuracy of 1.6mm, whereas
1,234.37 has an accuracy of 0.01mm, ie 160 times the accuracy.
The metric equivalent for your comparison would be something like 1234mm, which is hardly any more difficult to remember than 6-11/16". And even then it still has a higher accuracy (1.5 times)

Ralf

I would respond myself, but I will leave the response to Arthur Marcel, who is a Brisbane English teacher completing a Master's Degree at the University of Queensland and recently tried to build a shed using metric measures. He had a lot of trouble with botched cuts and waisted wood:

"Why? Yes, why? I didn't actually know why at the time. It took weeks of thinking about it before I even began to form an opinion. The conclusions I came to were twofold: firstly, there is the matter of short-term memory recall. Metric measurements are in the form of four digit numbers. There four-part 'packages' are quite complex in that they don't have a reserved slot in a simple human mind like mine. I mean I have pigeon-holes for all of the ten digits by themselves, and even up to every possible combination of two of them. However, there are 10,000 possible four-digit numbers, and for me they are just not quickly graspable. So either they had to be learnt by heart, a process which was slow and unreliable given the way an operation was continuously repeated throughout the day, or they had to be repeated over and over like a mantra while each measuring and cutting operation was performed, an equally unreliable process given the distraction factor. Writing the measurement down on an intermediate piece of paper was partly successful, however it was also slow, and I often got out of sequence. Fatigue and uncertainty was compounded by an increasing lack of confidence and the need to constantly recheck the number before putting steel to wood."

"Secondly, there is the matter of the metric distance scale. The standard metric tape that a prospective genius like myself buys in a hardware shop is not very well designed. As I said earlier, each centimetric division on my tape was subdivided into two half centimetric divisions which were in turn divided into five millimetric divisions. Now that meant that there were four millimetre graduations of equal height between each centimetre graduation (these being the tallest) and each half centimetre graduation (these being the next tallest). When trying to make an exact measurement with this kind of tape, the eye, which is after all the final arbiter of all human measuring techniques, no matter what the intermediate machine might be, has to make a logarithmic judgement as to where on this scale of up to four equally tall graduations the pencil must fall. Now with time to spare, a comfortable desk, and just one or two operations to perform, this is not such a difficult task. However, on a hot, gusty day, with a face full of perspiration, dust, hair and glare, it becomes truly eyeboggling. The most difficult measurements are those ending in either a two or a three, or a seven or an eight. These two graduations just blurred into one after an hour or so. Now I fully admit that it was my desire for exactness that led me to such fine measurement, however I feel it is a poor compromise to round everything off to the nearest five millimetres, something that I wasn't prepared to do."

"With the Imperial system I didn't have these problems. Firstly, the Imperial numbers were easier to remember. This was because each Imperial measurement is separated into two packets of easily graspable, one digit numbers, plus a packet of 15 possible fractions. There were 15 fractions because I was working to the nearest 1/16th of an inch, this being the thickness of my saw blade and as precise as I cared to go. Although I don't recall now, the only two digit number I could ever have encountered that week would have been eleven inches. What I do recall though was that not only could I consistently remember the current number but I could remember a lot of the previous ones as well, to the point of not having to refer to the plan for subsequent cuts of the same type."

"Secondly, the Imperial measurement scale is eminently readable. The inches are wide enough not to be crowded out by their indicating digit and the fraction scale is totally binary, meaning that there is only one subgraduation between higher order graduations, each of these being of correspondingly shorter height. There is no counting of graduations required at all."

You see, he didn't have to count because he could look at the inch and divide it into a fraction. We can, as I said before, intrinsically divide things into units of halves, thirds, quarters, eighths, and sixteenths by looking at something. And if he cared, he could measure everything in inches, (which is what I do when cutting lumber) so I would have measurements of 68 and three-quarters, which is easily memorable.
Don't take my testimony for it. Take an Aussie's who was on national radio.

If that bloke has got a Master's Degree, Ozzies should start worrying about the educational level of their universities...

Just because he has a Master degree does not mean anything. If his Masters degree was in Engineering orin Science, I would be worried especially as one of my friends is a professor at Brisbane. His subjectr was English - a subject which is not noted for its scientific or mathematical content.

I'm sorry, but what I see in the Australian posting is a closley argued, intelligent analysis of metric vs. Imperial measurments in relation to carpentry.

If, Conrad, Martin, you claim to be worried about the intellectual quality of what he says, please could you specify precisely where, if anywhere, his cogent argument breaks down

MattS wrote:

<<
Writing the measurement down on an intermediate piece of paper was partly successful, however it was also slow, and I often got out of sequence.
>>

I always plan my DIY on pieces of paper. First I measure up, commit the measurements to paper, do the design and then take my tools out. This iks just good engineering practice and nothing to do with metric or imperial units.

<<
Fatigue and uncertainty was compounded by an increasing lack of confidence and the need to constantly recheck the number before putting steel to wood.
>>

Why was he working when he was tired. That is how accidents happen.


<<
Secondly, there is the matter of the metric distance scale. The standard metric tape that a prospective genius like myself buys in a hardware shop is not very well designed. As I said earlier, each centimetric division on my tape was subdivided into two half centimetric divisions which were in turn divided into five millimetric divisions. Now that meant that there were four millimetre graduations of equal height between each centimetre graduation (these being the tallest) and each half centimetre graduation (these being the next tallest). When trying to make an exact measurement with this kind of tape, the eye, which is after all the final arbiter of all human measuring techniques, no matter what the intermediate machine might be, has to make a logarithmic judgement as to where on this scale of up to four equally tall graduations the pencil must fall. Now with time to spare, a comfortable desk, and just one or two operations to perform, this is not such a difficult task.
>>
1 mm is greater than 1/32 inch, but less than 1/16 inch. I therefore reject this arguement


<<
However, on a hot, gusty day, with a face full of perspiration, dust, hair and glare, it becomes truly eyeboggling. The most difficult measurements are those ending in either a two or a three, or a seven or an eight. These two graduations just blurred into one after an hour or so. Now I fully admit that it was my desire for exactness that led me to such fine measurement, however I feel it is a poor compromise to round everything off to the nearest five millimetres, something that I wasn't prepared to do.
>>
If his eyesight is not up to scratch he should consult his optician and not blame his tools.


FInally

The ozzies are always going on about the whinging Poms. This should like a whinging Ozzie.

"I'm sorry, but what I see in the Australian posting is a closley argued, intelligent analysis of metric vs. Imperial measurments in relation to carpentry."

Maybe because he agreed with you?

The "bloke" that did that thesis was a leading advocate/proponent/introducer of metrication in Australia, btw.

Something which he turned out to regret.


I'm interested that no-one mentioned that!

"1 mm is greater than 1/32 inch, but less than 1/16 inch. I therefore reject this arguement"

What a dumb statement. The argument was not that 1 mm was too small to see, but that 1 mm next to 1 mm was too hard to see. On an imperial tape, you never have to count sixteenths because if you do, then you are at a larger fraction the moment you add one, so you never have to distinguish between 2/16 and 3/16. Why? Because 2/16 is 1/8 and 1/8 has a larger line on the tape than 1/16 incriments do. Furthermore, most carpentry is good enough to the nearest sixteenth, so your argument that the size of a mm is smaller hurts you more. Sixteenths are the smallest comfortable size on the imperial scale, so why would one want to read an even smaller division?

One of the dangers of using sixteenths of an in is that if you write "1 1/16", you run the risk of reading it as "11/16". This problem does not arise whien using metric units. When writing this measurement in mm, one needs two characters instead of six (counting the space as a character).

You know the arguments are getting bad when it gets to how you write the numbers.

One of the dangers in using the metric system is when you write the numbers you may get the decimal in the wrong place. C'mon, if you can't find any falicy in my logic about customary measures and all you can argue about are the pitfalls of writing 1 and 1/16 then you really need to just admit defeat.

The correct way to write one and one sixteenth is:

1-1/16" Or more preferably where the one is directly over the 16 and the whole one is larger. Honestly, this is going back to grade school folks. (achem Martin)

I'm waiting for that "default lost the argument response" now from Martin and his "rules" (no offence, Martin!).

Lets see,

Ohe yes! 1-1/16" is actually one minus one divided by 16 minutes.

Looking forward to it.....

In my junior school days I was taught to write the first "1" is large letters and the subsequent "1" and "16" in small letters with the "1" vertically above the "16" and a horizontal line between them. I was never taught anything else.

My children have not been taught the minimum concerning vulgar fractions - they are difficult to use on a calculator.

As regards losing the decimal point - I never use a decimal point in carpentry. ALso, havoing spent three years on the Continent, I tend find myself using a comma instead of a dot as the decimal separator. In critical areas where the lost of the decimal separator could be serious and where it would not be picked up immeadiately, one must of course take extra care or design one's system such that it is failsafe. AS an example - I am diabetic and as such measure my sugar levels regularly. In the UK, sugar levels are usuallu recorded in mmol/litre and I endeavour to keep my sugar between 4 and 7 mmol/litre. In Germany, the units used are mg/dl and the corresponding levels are 72 to 126 mg/dl. If my sugar level were to drop to 1.1mmol/litre, I would be is a bad way and would need instant help. If on the other hand my level was 11mmol/litre, my sugar would be high. In the short term, there would be no ill effects, but if my sugar remained at this level long term, damage would result. AS can be seen, there could be a problem if the decimal point was lost. In Germany this scenario woudl not arise because the units have been chosen so as to avoid decimal points.

Likewise, in engineering, one only uses decimal points in prescision work, so the problem seldom arises.

Finally, consider these two expressions: 11-13/16" and 297mm. The first is eight character (excluding the units) and the second is only three charactres (excluding units). It is noted on course that one does not write the units down in engineering drawings when using the metric system.

My high school teachers would say that you Martin are too calculator dependant, and that my friend means you can't use your brain. The only reason you don't like fractions is that you can't do numbers in your head. Why? Because you rely too much on a calculator. Furthermore, the only reason that a base ten system seems to be superior in your mind is that our numerical writing system works that way. Need I remind you that a binary number system is how a computer works.

I hated fractions in school because I thought they were too difficult to work with. That was only because I was a calculator junkie. When I stopped using a calculator and started using my brain, I noticed that I became better with numbers and better with fractions.

Lastly, your bit about the inch problem? Well one could always write out 11.8125" and that avoids the fractional problem. But, it's already been proven that people can visualize fractions and not decimals. The problem with your metric system is that fractions are not possible, but in customary measures fractions *and* decimals are allowed.

I don't know what world you live in Martin, but when I do a site plan (I'm a Civil Engineer)in metric, I write the units on the drawing since all my bearings would be measured in meters and my pipes in millimeters. Among other things such as offsets for stations which would be in meters, not millimeters. It would be rather confusing otherwise.

It is common practice for Engineers (and even Architects) to not put the dimension units on their drawings.

It simply isn't necessary.

For instance, a note calling up a pipe as "450 dia" obviously means millimetres, not metres.

I know you yanks like things big, but I don't you make pipes quite that big.

A dimension between building grid lines would simply be marked 6000.

Again, it's obviously in millimetres so there is no need to add "mm" at the end.

The only real exception to using millimetres is with floor levels and external spot levels.

For example, " FFL 28.150 " (levels tend to given to three decimal places to represent the millimeters, even if the last digits are zero).

Once again it is obvious what the unit is. Nobody is going to give a level to three decimal places in millimetres.

MattS wrote
<<
I don't know what world you live in Martin, but when I do a site plan (I'm a Civil Engineer)in metric, I write the units on the drawing
>>

I live in a world where metric units are the norm in engineering and where conventions have been developed that remove the need to actually write the units.

If you look at the European version of most car handbooks (UK included) you will notice that few, if any give the units of measure in their drawings. For example, the drawings of my VW Golf show height as 1410, width as 1640 and length as 4250. One does not need a degree in rocket science to deduce that these measurements are in mm. If you wish to convert to meters, the cars height is 1.41m, width 1.64 and length 4.25

I have a rover
Both units are used.

I used to have a Lotus, that was mainly imperial

We have similar conventions here with certain things such as elevations above sea-level, which we all know will be reckoned in feet. However, not putting units on things is completely careless work (as my professors and collegues would tell me).

Anyway, I could care less whether or not you put your metric units on or not. You still have not grasped the idea that fractions, which are extremely visual and liked by a majority of humanity, are not legal in your metric world. You see the fraction is everywhere and easily recognizable. In customary units both the fraction and the decimal are acceptable and useful since the system was designed to be easily halved, quatered and such.

Why was it done this way? Constanly people find the need to do this with quantities they use every day. The customary measures were created the way they were for the convenience of the human being. His/Her closeness to the work or the commodity dictated the size and system of the units.

Furthermore, there is a problem with the size of the metric units. The meter is too long. The centimeter is too short, the millimeter is way too short. The foot is the right size for measuring things.

Your example of giving sizes in thousands of millimeters still is annoying to me. 8", 10", 12", 16", 18", 20" pipe is still easier to say and to write. You would have to write 200, 250, 300, 400, 450, 500. Your numbers have, count them 3-5 sylables not including units. My numbers have 1-2 not including units. Not only that, but the millimeter is the most inconvenient size for anything I could think of that I would measure in my work. The inch, something I carry around on my hand (a reason why it's so convenient) is a move convenient size with which to work.

I had to chuckle this morning

While waiting for the train I overheard some french girls talking in english about how cheap the make-up they bought was.

One said "and zis foundation is was only three and a half pounds!"

Someone remind me where they invented that bleedin' metric thing again???

<<
One said "and zis foundation is was only three and a half pounds!"
>>

Which is just over five Euros (and dropping when measured in Euros)

Well they seemed to be getting a kick out of using pounds!

Interestingly not one of them said "...thats about nn euros"

Perhaps like most europeans they are growing to hate mickey mouse money!!!!

You know, I find that it's very interesting that no one seems to argue with me about the convenience, easy visualization, and overall superiority of the foot and the inch and their customary fractional divisions. I also liked the bit about the chain and our discussions there, but when I pointed out how Gunter was a genius in his design, no one complained either.

The argument always seems to stall at that point and I think it's because you metricators cannot admit to ceding that point. What do you think Steve?

SteveH: "Perhaps like most europeans they are growing to hate mickey mouse money!!!"

Steveh, my last holiday was in Turkey and after a few days I was already saying "wow, that's only 6 million", "that's cheap, it's only 2.5 million", etc.

Does that mean that I hate the £ Sterling ?

MattS: "The argument always seems to stall at that point and I think it's because you metricators cannot admit to ceding that point. What do you think Steve?"

Simple answer to that, mate, it's hard to argue with "common sense", see Conrads effort above for proof. Do you think they get paranoid that they will be letting their side down every time they:
1) Order a pizza, "I'd like a 9 .... a 9.... a [hangs up phone]"
2) Cut the pizza, "Ok if I lay the protractor down thus I should be able to...."

Conrad: Congratulations once again for missing the point so wildly that the point is now at the other end of the universe.
Come off it! Are you saying that the average Brit abroad doesn't say something like "300 euros for that camera, that's not bad - thats about 200 quid!" or "Mavis, this hard core specialist adult video is 40 dollars, what's that in pounds?"

Go back and see if you can discover the "point"

hint 1: look for the fraction
hint 2: look for the lack of wanting to know the equiv in euros.

(jeesh folks, can't I make it more blunt/clearer?)

Steveh: "Are you saying that the average Brit abroad doesn't say something like "300 euros for that camera, that's not bad - thats about 200 quid!" or "Mavis, this hard core specialist adult video is 40 dollars, what's that in pounds?""

Congrats Steveh for completely missing the point !

All I'm saying is that the fact that those French girls do not mention the equivalent of that make-up thing in euros doesn't mean they don't like their own money ! When I spend 10 days abroad, I don't need to calculate anymore how much something is in pounds: after a couple of days I JUST *KNOW* IT ALREADY. (Of course this is not the case for high prices such as for cars, houses, etc.)

"Congrats <name> for completely missing the point !"

Please use freely, there is no charge.

So typical of you Steveh...
No counter-arguments anymore ???

Counter arguments for what Conrad? This money discussion is the stupidest I have seen on the boards. You had no argument to counter. It's obvious that you still have no response to *my* argument about fractions (maybe because you had trouble with them in school too). I can't think of anything more obvious to your ceding my point.

BTW, Steve, make Conrad and Martin divide your 30.48 cm pizza into tenths.

I don't understand how imperial measurements help you with that, especially since we all use the same scale for angles...

Ralf

Ralf, the argument was about fractions and I was merely showing that fractions out do decimals anyday. When you divide a pizza, it is almost impossible to do it with the naked eye accurately into tenths. I was using the example to show how binary fractions are natural and decimal fractions aren't.

How many times do you divide something in half, and then in quarters, and then in eighths? That was what the pizza illustration was showing.

First of all, apologies, I am now told the spelling is *burnicle* not bernicle.

I am further informed that the burnicle is named after a Mr Burnicle, who devised it in the 1970s, er, because the metre was too long for reckoning and the centimetre too short.

I understand that a common feature of British timber yards is the 'Two Burnicle Rule', which is, er, precisely 66.66recurring centimetres long, made of steel of course.

It's calibrated on one side into six even divisions, i.e. each about 4", or a handbreadth, whilst on the other side it is divided into 20 units - not far off an inch each (about an inch and a quarter).

There is then a simple formula for converting 'square burnicles', multiplied by the thickness of the wood in millimetres, into cubic metres (in which much wood is sold these days).

More details will be posted as they arrive. I can find nothing about the burnicle, nor its originator, using my search engines on the Internet

MattS wrote: "It's obvious that you still have no response to *my* argument about fractions (maybe because you had trouble with them in school too)."

Tell me Matt, what is the best way to write the following:

14/63 of 100 or 22.222222... ?
27/141 of 100 or 19.1489... ?
55/21 of 73 or 191.190... ?
87/103 of 1862 or just 1572.75... ?

In all cases I'd prefer the second way of putting it. Why ? Because decimals are nearly always easier to visualize, except for halves, thirds and quarters of course, which are exactly as easy to envisage as decimals.

BTW: I *loved* fractions at school...

For anyone who hasn't noticed, decimals are fractions, only for an agreed denominator.

Matt,
"When you divide a pizza, it is almost impossible to do it with the naked eye accurately into tenths."

So it is for thirds.
Or fifths.
Or sixths.
...

I would like to see an example though:
How do you divide a pie into 3 equal parts easier with Imperial measurements than with metric ?
Just because you have a new name for a third of a yard doesn't make it any easier to divide it by three, does it ?

I for one find it *much* easier to tell the difference between 0.75 and 0.718 than between 12/16 and 23/32.
I can also add them easier.
Or multiply them without ending up with an outrageous denominator.

Ralf

Actually, while re-reading my previous post, I noticed the following:

0.75 * 0.718 ?
I can tell you right away that's going to be around 0.5 .

12/16 * 23/32 ?
Who knows what that is...

Ralf

It was a government Minister who grumbled:

"The trouble is that half of the population don't know what 50 per cent means".

There's quite a lot in that remark

On visualisation, many people say that they find the continental way of describing steep hTony ills - in percentage terms - much less easy to visualise than the British way of doing it - to say how many units along for every one up.

In fact, there is still a significant proportion of steep hill signs in the U.K. using the British system (at a rough estimate I would say between 5% and 10% (er, one-twentieth and one-tenth).

The record steep hill I have ever seen in the U.K. is one that leads down from Harlech Castle to the main road - 40%. We have driven down it successfully but didn't attempt to drive up it

How would I write 14/63 of 100? I would certainly not write it as a decimal, because the moment you do, it becomes inexact. Didn't you learn anything in mathematics?

22.22 or 22.222 or 22.22222 or 22.2 with a bar is not acceptable. 200/9 is the correct way of writing it.

2700/141 or 19 & 21/141 are correct. The moment you truncate your decimal, it becomes in exact. The preferable way that I was taught to write it would be as the improper fraction of 2700/141

The same for all the rest of your examples.

Now as to Ralph's comments. It *is* much easier to deal with a yard of 36" because 36 divided by three is an even number. It's more than a new name, it's an actual unit. Since there are 36" in a yard, that means that 1/3 of a yard is 12 even inches or a foot, not 33.333333333333333333333333333333333333333 cm as in a meter.

In all history, groups of people used measurement systems that can be divided by at least 3 ways. YOur metric 10 is only divisible by 2 and 5. A foot of 12" is divisible by 2,3,4,6.

Now, since you complained about fraction adding, and your example was 12/16 and 23/32, you obviously cannot see beyond the end of your nose. 12/16 is really 3/4. 3/4 of an inch is very easy to see. Since I know that 23/32 is almost 24/32, 3/4 as well then your hard problem becomes extremely easy.

(3/4)+(3/4)=(5/2) (approx.) and you only have to subtract the extra 32nd if you want to be exact. We would say that 5/2 is good enough for government work.

(3/4)*(3/4)=(9/16) or 0.5625 compare (12/16)*(23/32)=0.539

It's again close enough for government work.

Once you begin to stop thinking about decimal equivalents for things and begin seeing the fraction then the math with the fraction becomes a cinch.

That last post was me. Sorry....

"The record steep hill I have ever seen in the U.K. is one that leads down from Harlech Castle to the main road - 40%. We have driven down it successfully but didn't attempt to drive up it."

'We', is that the Royal party?

The steepest I have seen is 25%. On that occasion the signs were dualled with those which said '1:4'.

Matt,

your "33.3333" stuff:
My point was that the physical action of dividing it by three is not any easier just because you have another unit called the foot.

Concerning my example of fraction multiplication vs decimal multiplication:
To get my approximate value I had to one calculation : 0.7*0.7.
Then see that it is a bit more and know that it is around 0.5.
You had to do several multiplications and findings of common factors to get to the same result.

Well, what about 5/16*13/32 then ?
0.31*0.4 ~ 0.12, very easy.

Ralf

The metric system is NOT based on divisions of 10, but rather of 1000.

As a result, a 1000mm metre is divisable by 2,4,5 and 8.

Also, a third of a metre can quite adequately be expressed as 333mm and two thirds as 667mm.

Only the most perdantic would worry about a 0.33(recuring)mm error. It's less than the width of most pencil points and STILL more accurate than the fabled 1/16th of an inch.

Besides, MattS. Why, as a Civil Engineer, are you so worried about accuracy ?

One of my old lecturers at college used to have a joke:

Q. What will an Engineer say when you ask him "What's two plus two?" ?

A. "About five"

The physical dividing by three is easier since I have a foot. If I have a board a yard long, then dividing the board into thirds is a piece of cake. If I have a board one meter long, it's impossible. The number 12 is a beautiful number since it's divisible by more numbers than the number 10.

When doing construction or carpentry I have never multiplied lengths in inches before. So your examples of fractional multiplication in inches are not applicable to that. When figuring square footage I may multiply lengths together, but in that case, I'm dealing with 6' by 3' maybe or at worse case scenario 4'4"x3'6" and in that case it's very easy to do the multiplication too since I know that 4" are 1/3 foot since there are 3 4's in twelve and 6" are half a foot.

I'm not saying that decimals are bad. I'm just saying that binary fractions are more preferable for most people to visualize. You have to take yourself back to times before there were calculators. You're so tied to a calculator that you can't see that people are not interested in multiplying things together, they're interested in dividing them into parts. The units of the customary measurement system were created to make dividing things easy.

Example:
You go to the dairy. You say to the dairyman, "I would like some milk."
He says, "How much?"
You say, "Oh well what are my choices."
He says, "Here is the one gallon size."
You say, "That's too much, but I think I would like about 1/4 of that."
He replies, "Well that's a quart." He then hands you a quart container.

In your metric world, that would be impossible. You see, the person likes the way 1 quart sounds and he can see that it's a quarter of the larger size that the dairyman showed him originally.

The beauty of the customary measure is that each fractional part is another *single* unit. People like single units of things. We tend to divide things in our world into fractions (like the pizza) and while I can't have a size that is divisible into every preferable fraction, I can get closer with numbers like 12, 16, 2, 4, 8, and so on. Whereas 10 does not work for that stuff.

That's why half of one thing is one of something else and a quarter of one thing is one of something else. It goes back to when people were more tied to the commodities which they were measuring.

You're interested in doing abstract calculations with numbers that you can easily manipulate on your calculator. That's ok for science. The rest of the world only wants half a pound of banannas because that's a convenient amount for my kitchen fruit basket, and half a pound is easier to say than 0.227 kilos.

That was me above...

I, for one, find it marginally easier to do arithmetic with fractions in my head.

To use Ralf's examples:

0.75 * 0.718

Ralf knows its "about .5". Fine, so do I. But only because I interpret .75 as 3/4, and round .718 down to .7. Then I can do (.7*3)/4 = 2.1/4 = 5.25. But this is not the exact answer, merely an approximation.

To I could do (.718 * 3)/4, which I must then expand to [(.7*3)+(.010*3)+(.008*3)]/4 = (2.1+.030+.024)/4 = 2.154. Then I still have to divide that by 4. At this point, I'm ready to look for an easier way:

12/16 * 23/32

This is hardly difficult.It's (12*23)/(16*32). If you don't know these instantly, it's easy to work them out:
12*23 = (2*12^2)-12 = (2*144)-12 = 288-12 = 264. 16*32 = 2*16^12 = 2*256 = 512. Simplify to 132/256 = 66/128 = 33/64

This is the exact answer, (and the initial value of 23/32 is also exact, unlike above, where it is truncated to three decimal places) and it takes all of ten seconds to get to it in one's head. And attempting to actually multiply out .75 * .718 without the use of fractions would be too tedious to do.

16*32=2*16^12=2*256=512.

Right answer for the wrong reason.

2*16^12 = 2*281,474,976,710,656 ...

Mr Marvel the measuring man has a super duper imperial tape measure with which he can measure things exactly however small. He likes fractions too.

He is also miraculous at constructing things exactly.

One day Mr Marvel produces a perfect rectangular wooden panel 24 inches by 12. Out of curiosity he measures the panel from corner to corner exactly in inches and fractions of an inch.

What is the result?

The distance from one corner to the other (e.g. top L.H. corner to bottom R.H. corner) is:

26.832815 inches


calculated as follows:

24 squared = 576

12 squared = 144

total = 720

hypoteneuse is square root of 720 = 26.832815 inches

or very close to 26 and 5/6 inches

Anonymous:

Under the conventional order of operations, exponential operations are carried out before multiplacation or division.

Thus, 2*16^2 is equivalent to 2*(16^2), not (2*16)^2.

<<
One day Mr Marvel produces a perfect rectangular wooden panel 24 inches by 12. Out of curiosity he measures the panel from corner to corner exactly in inches and fractions of an inch.

What is the result?
>>

12*sqrt(5) inches.


There is a mathematical theorem which *proves* that sqrt(5) cannot be an exact fraction. (It might get very close to being an exact fraction, but will never be an *exact* fraction).

Mr Marvel is therefore eitehr ill-informed or a con-man.

martin: There are plenty of irrational numbers. But any number that cannot be expressed as an exact fraction also cannot be expressed as an exact decimal, since decimals are simply fractions in which the denominator is a power of ten.

However, as you increase the precision of your approximation, the decimal representation will grow increasingly complex, whereas the fractional representation, with any denominator allowed, will remain comparatively simple.

Rotclar,

I agree with what you said, but you should also agree that even if you were to aproximate sqrt(5) to 100 decimal places, I could still define it more accurately. If you wer to use 1000 terms, I could still write it down more accurately and so on. In pure mathematical terms, this means that an exact solution does not exist. (PS, I have a degree in applied mathematics, I do not know what your mathematical understanding is, so I am trying to keep it simple).

I was correctly taught that if one wanted to be exact, then the *only* way to write the answer would be 12*sqrt(5). Thus there is no room for decimal approximations or anything else.

Thus the distance from corner to corner would be "12 root 5 inches" and nothing else is correct. All other answers are approximations no matter how accurate.

Of course, I am just an engineer Martin and since most mathematicians believe engineers are full of bunk, you may not like my answer.

>However, as you increase the precision of your
>approximation, the decimal representation will grow
>increasingly complex, whereas the fractional
>representation, with any denominator allowed, will
>remain comparatively simple

Rotclar,
I find that a pretty outrageous claim.
Could you please demonstrate that with the example of sqrt(5) ?

Ralf

<<
Thus the distance from corner to corner would be "12 root 5 inches" and nothing else is correct. All other answers are approximations no matter how accurate.

Of course, I am just an engineer Martin and since most mathematicians believe engineers are full of bunk, you may not like my answer.
>>

Matt, I agree fully with your answer and I could not have put it better myself. Your answer shows that Marvel's assertion at the start of this posting was incorrect.

BTW, Although my initial degree was in Physics and Applied Maths, I am also an engineer, having had my membership of the [British] Engineering Council put forward by the British Computer Society.

"Of course, I am just an engineer Martin and since most mathematicians believe engineers are full of bunk, you may not like my answer."

LOL

The correct answer to the above problem is that an *exact* fraction representing the distance from corner to corner does not exist. Even Mr Marvel with his special tape measure cannot do it.

Well done to those who spotted that the calculated result (from applying the theorem of Pythagoras to the right triangle formed by two adjacent sides and a diagonal) is sqrt(12^2 + 24^2) = sqrt(144 + 576) = sqrt(720) = sqrt(144 * 5) = 12*sqrt(5) - is irrational.

An irrational number is so called because it cannot be represented as a rational number i.e. an explicit fraction or a decimal with recurring or a finite number of digits. As a decimal an irrational number has an infinite sequence of non-recurring digits.

Irrationals can be approximated to any degree of accuracy you choose by a fraction with a large enough denominator (reduced to its lowest terms) or by a decimal rounded to a sufficient number of places.

So whats the big deal? Well consider this. How can the distance between the corners of a rectangle be so indeterminate? (Unlike the length of its sides).

You might reasonably argue that there is no such thing as an exact measurement in the physical world since they are always subject to a finite degree of precision (plus/minus something however small) and as such are only ever approximations to their idealised geometric counterparts in the abstract world of mathematics (where lines are always perfectly straight and have no thickness etc).

The trouble is we have a case where even in that ideal world we still dont know exactly how far apart those corners are!

>However, as you increase the precision of your
>approximation, the decimal representation will grow
>increasingly complex, whereas the fractional
>representation, with any denominator allowed, will
>remain comparatively simple

Out of boredom here at work, I just sat down and wrote a small Perl script, spitting out the following:

sqrt(5.0) = 2.236067

2.2 = 11/5
2.23 = 223/100
2.236 = 559/250
2.2360 = 559/250
2.23606 = 111803/50000
2.236067 = 2236067/1000000

Well, so much for the "comparative simplicity" of the fractions...

Ralf

If people worked primarily in fractions they might say sqrt5 is approximately 7303/3266

Ralf suggests they would say 2236067/1000000

But Ralf's fraction is not as precise an approximation!

Besides *as fraction* (without the positional shorthand notation) it is more cumbersome. It has
more digits and makes fractional notation look worse
than it is.

There seems to be some error either in Ralf's arithmetic or his reasoning.

Because if you square the fraction he proposes, 2236067/1000000, you get something which is 0.9 ppm too small.
But if you square 7303/3266 you get something which is 0.5 ppm too big! The approximation is better and it is not so cumbersome!
So for some reason, perhaps carelessness, the "Perl script" casually generated by the bored programmer did not adequately test the idea of using fractions to approximate square roots.
Logically it does not justify the "Well, so much for the comparative simplicity of fractions" conclusion.

Base ten positional notation is a wonderful cultural invention which was introduced into Europe by the Pisan mathematician Leonardo Fibonacci in the decades around 1202-1228. He got the idea from Arabs who may in turn have picked it up from Indians. A civilized person might be expected to use either notation elegantly---that is, without spilling his soup in his lap.

For reference, the previous post:

Rotclar said
>However, as you increase the precision of your
>approximation, the decimal representation will grow
>increasingly complex, whereas the fractional
>representation, with any denominator allowed, will
>remain comparatively simple

Ralf replied
[Out of boredom here at work, I just sat down and wrote a small Perl script, spitting out the following:

sqrt(5.0) = 2.236067

2.2 = 11/5
2.23 = 223/100
2.236 = 559/250
2.2360 = 559/250
2.23606 = 111803/50000
2.236067 = 2236067/1000000

Well, so much for the "comparative simplicity" of the fractions...]

I'm absolutely aware of the "flaw" of my Perl script.
The way it works (and which is also discernible from the output) is that it takes the value 2.2, converts it to 22/10 and then tries to find common denominators to simplify it, printing the simplified fraction at the end. Then it goes on doing the same with 2.23, 2.236 etc.

As you can see, the series 2.2, 2.23, 2.236 etc. is derived from the decimal approximation of sqrt(5).
It is obvious that there are always fractions that get closer to sqrt(5) than any given decimal representation, as much as there will always be a decimal closer to sqrt(5) than a given fraction.

What I was mainly pointing out with my Perl script is the fact that, if you want to use fractions when doing this, you end up with ever-changing denominators, which strips pretty much all usefulness from them.
That's the trick about decimals:
They are also simply fractions, but with an agreed on denominator, which makes many neat things only possible (or at least makes them *way* easier), for example the most basic operation of them all: Addition.

Ralf

Dear fraction lovers, check this out:

9/4 ~ 2.2
38/17 ~ 2.23
161/72 ~ 2.236
682/305 ~ 2.23607
2889/1292 ~ 2.236068
12238/5473 ~ 2.23606798
...

there's more.

How were the above fractions calculated and what is the next one?

P.S. They were not derived from approximate decimal equivalents.

this is delightful!
whatever your persuasion as to units issues,
please think of something you might like
to post at Junk the Metric System! forum
http://www.network54.com/Hide/Forum/214108
Any lively mind welcome but this of Teaser's
is especially meritorious. Also Bryan you
said you were going to base pound on u.
Put a post about it at Junk Metric please!
It is the "atom counters" approach--some people
want to base kilogram on the atomic mass unit---
and a definite possibility.

51841/23184

when I square it on my calculator I get
5.000 000 002

Well done Leonard, spot on.

Can anyone else see how Leonard did it?

Hint: Look at each numerator and see how they relate to the previous 2. Do the same for the denominator.

I've now got more information about the burnicle and its use in calculating the area and volume of timber.

To recap, the metric system. with its over-large metre and its too-small centimetres, was quite unsuitable for measuring timber, so a Mr Burnicle, about 30 years ago, invented a new linear measure, er, the 'burnicle'.

The 'burnicle' is 0.3333recurrung metres long (one-third of a metre).

This is how it works.

An awful lot of timber is supplied in planks. These planks are so many feet long and usually so many inches wide, usually under 12 but sometimes up to 24 or so.

In the good old days, timber-measurers would measure the length of planks in feet, the width of the plank in inches, multiply the two figures, and then divide the result by 12 to get the number of square feet. Simple.

With the introduction of the metric system, in came the 'burnicle'.

Timber-measurers use a two-burnicle rule, i.e. one that is 0.6666recurring metres long (two-thirds of a metre).

The two-burnicle rule is divided into twenty-two divisions which, as far as I know, have no name, so I'll just call them 'units'. These are then sub-divided again into thirds.

If you work it out, each 'unit' is 0.0303recurring metres long - or 3.0303recurring centimetres - or one thirty-third of a metre.

So what you do now is count the number of burnicles along the length of the plank, and multiply by the number of 'units' of width. For every 100, the answer comes to 1 square metre - well, nearly.

To take two examples.

A plank is 5 burnicles long (1.6666recurring metres). It is 20 'units' wide (60.6060recurring centimetres).

Multiply 5 by 20, and you get a hundred. Hence the plank is 1 square metre in area.

Or take a plank 8 burnicles long and 12.5 'units' wide. The plank is 2.6666recurring metres long and 37.8787recurring centrimetres wide.

Multiply the 8 by 12.5 and again you have 100, i.e. 1 square metre.

Checking the answers, the error rate is approximately 1% over, i.e. this ingenious method still produces a measurement of area of about 1% over the true metric area.

But what does a bit of error matter as long as you're using the metric system?

Tony, the problem lies in your basic defintion.

1 Burnicle = 1/3m
1 unit = 1/33m

So a plank with a length of 1 burnicle and a width of 1 unit has an area of 1/99m^2, not of 0.01m^2 as your previous posting seems ot pre-suppose.

The error of 1% lies in your poorly defined systm and has nothing to do with the metric system.

Tony, do you think you could produce any online proof for your burnicle ?

Ralf

Yes, a plank one burnicle long (1/3rd metre) and one 'unit' wide (1/33rd metre), when you multiply them, comes to 1/99th square metre instead of 1/100th.

In other words, just like I said, it comes to just *over* one square metre, almost exactly 1.01 square metres.

Rememebr it's not *my* 'poorly defined units', but someone else's, which happen to be in widespread use in the timber industry.

I can find no reference to the 'burnicle' searching the internet, but will attmept to discover if there is anything in writing and gladly post details of what it is and where to get hold of it.

I daresay it would be fascinating to track the original Mr Burnicle down and ask him why he invented it.

My relative has now presentd me with a complimentary one-burnicle steel rule. It's divided into just three units on one side and into eleven major and 33 minor units on the other side.

This weird measuring system may not be as daft as it first appears.

Clearly it was designed to ease the calculation of area in square metres without a mechanical/electronic aid (the technology was much more expensive 30 years ago) in this particular application.

The systematic error of 1% is in the customers favour when pricing and re-selling by this method.

This may have been a convenient way of meeting legal obligations when selling a commodity per unit of measure. It perhaps guaranteed that random errors in measurement and cutting were compensated for.