Vic Tesolin weighs in on the metric debate
The argument that “it’s just as easy” to work in fractional inches over metric is ludicrous
The metric system has been around for a long time—since the 1790s to be more accurate. In fact, it was around prior to the current imperial measurements that we seem to have trouble leaving behind. It all began in France, and the metric system has become the world standard for measurement. As a Canadian, I live in a horrible measurement world where only some of the things are in metric, and we aren’t alone. The Brits straddle both systems as well.
The USA seems to get dumped on over the metric system because they refuse to make the change. Canada half-made the change in the 70s, while countries like Sweden made it illegal to trade in imperial measures so they are now completely metric and loving it. Many woodworkers seem to be the stalwart, last guard of the imperial system. But why?
Mike Pekovich said recently in a FWW podcast episode that his trouble is that he thinks in imperial so that’s what he sticks with. I think Mike has hit the nail on the head. In order to switch from one to the other, you have to train your brain to think in metric. It’s like learning another language. I think in English but can speak a bit of Italian because of my upbringing. Because I don’t think in Italian, I have to think of what I want to say in English, then translate to Italian, then hope I don’t offend someone when I speak.
I have made the switch. At first it was a matter of necessity because I write for woodworking magazines around the world that use the metric system. But then I started experiencing the joys of dumping the imperial system. There are people who profess that it’s easier to work with fractions rather than decimals. I’m not going to lie; I don’t understand this. Let’s take a look at some examples:
Adding 1-5/16 in. + 1-5/16 in. + 3/8 in. + 3/4 in.
This requires many steps:
- Pick a common denominator – in this case we will use 16ths
- The fractions gets converted to improper fractions (21/16) + (21/16) + (6/16) + (12/16)
- Then do the arithmetic, all over 16ths 60/16
- Then convert to a mixed fraction 3-12/16
- Finally, reduce the fraction 3-3/4”
You can also work in the imperial system but use decimal inches which is the numerical expression of a fraction. To my mind, this makes the math much easier because it’s one step.
With decimal inches it more simply looks like this:
1.31 in. + 1.31 in. + 0.38 in. + 0.75 in. = 3.75 in.
And finally, millimeters, which is just as simple as decimal inches but doesn’t require any conversion:
33.3mm + 33.3mm + 9.7mm + 19mm = 95.3mm
The argument that “it’s just as easy” to work in fractional inches over metric is ludicrous. It’s quite clear which is easier. Since I have trained my brain to think in millimeters, my woodworking math has been much easier. No more multiple steps, fewer transcription errors (5/32 instead of 5/16) and I can just focus on the woodworking. In the end, work with whatever system you want or even better, ditch the numbers altogether and work referentially. We’ll save that for another time.
In order to understand, you must do – V
Comments
Like Mike Pekovich I think in imperial; thus, I still use it. Plus all of my measuring tools are in imperial. You can not convert from imperial to metric. Don't even try it. One of the hardest aspects is that the metric system, other than liquid, is all based on the meter which is a bit more than 3" more than a yard. In imperial we think in feet - less than a third of a meter. But, do you think of a mile as 5,280'? Probably not. On the other hand, the metric measure on the highway is the kilometer - 1000 meters. Kilo means 1000, except in computers. That's another topic. Now, going for smaller? We have deci means 1/10, centi =1/100, milli = 1/1000. So, a decimeter is 1/10 of a meter, centimeter = 1/100 of a meter and millimeter = 1/1000 of a meter. Put in another term, decimeter=.1 meter, centimeter=.01 meter, millimeter=.001 meter. You're just shifting a decimal point. Most metric measuring tools are already subdivided down to millimeters.
As was mentioned, if you think you'd like to go metric, it's all or nothing. Take a class in metrics at a local college. That will make it easier.
I think your fractional example is disingenuous. For me its all about proportions and the commonly used denominators. Specifically the foot with its increased factorability makes it easier to think about things in terms of common proportions we use 1/2, 1/3, 1/4. I think if we could go back in time the perfect system would have set the metric system to a duodecimal number system (base 12 vs 10).
How does the foot have increased factorability? Unless you're really good with dividing by 2s, 1/16, 1/32, 1/64, 1/128, 1/256, etc. A foot does divide by 2, 3 & 4 quite nicely. But, let's say you need to take 1/3 of a foot. That's 4". Now, you need to take 1/3 of that. That's 1.33333 ad infinitum. It also doesn't come up with even 8ths, 16ths, 32nds, 64ths, etc.
We use base 10 because we have 10 fingers. We don't get into the semantics of 8 fingers and 2 thumbs. I can work in base 2, base 8, base 10 & base 12 quite easily. But, I'm a computer operator & programmer. It's necessary.
My house is imperially built, so is my furniture.
When I was a kid in school in the 60s and 70s it was all about how the US would convert to the metric system, so we learned it. I worked on machinery most of my life, using both systems and the Whitworth thrown in for good measure (pun intended).
I'll stick with my comfort zone, thanks.
As for math with fractions, I have a great fraction calculator on my phone that works really fast. No common denominator required.
I don't get it, either, Vic. Whether it's fractional imperial, decimal imperial, or decimal metric, that little addition problem was easily calculable in real time.
It's using the values where the problem lies. I intuitively 'know' imperial measurements, and how they relate to the world. Until I would fully internalize and become 'fluent', metric measurements are just numbers without meaning. You may as well suggest I have all my woodworking conversations in French. Why? To say I can, I guess...
It's a fun debate, but speaking the Imperial language is the same skill as speaking Metric. For example, I would never do the Imperial summation the way you explained. When I know my tolerance is 1/16, I simply record everything in that fraction to begin with:
1-5/16 + 1-5/16 + 6/16 + 12/16
Then just add the numerators by sight: 5 + 5 + 6 + 12 = 28/16
I know 2" of 1/16ths is 32. So the 28 is 1" plus 4 less than 16 of them: 12
Added to the two original inches: 1 + 1 + 1 + 12/16 = 3-3/4
Also, you can't divide by 3 in the Metric system either, so 1/3 of a meter and 1/3 of that is going to be a fraction. (Even a millimeter is too large to round without cumulative error for any precision woodworking after just rounding just one or two dimensions.)
The counter argument is fine, I often work in millimeters to simplify connections to metric hardware and have designed entire buildings in metric. But the Imperial system has a pretty impressive logic that isn't immediately obvious until you speak it fluently.
Finally, I believe the real culprit behind the delayed US changeover is the construction and real estate industry. We own a massive real estate market designed 100% in the Imperial system. The logic of our building codes and the legal surveys establishing property ownership are all in the Imperial system. 2x4s, even though they are nominal sized, are still derived from Imperial inches. I don't know how we'll ever migrate short of importing 100% of our products (like plywood), that arrive in port with "hard" metric dimensions. I'm afraid doors will be 36" wide (914.4mm) for a very long time to come.
It’s a funny debate because one system is no better than the other. Also, the example you gave with the multiple fractions only took me a few seconds to figure out. It’s really not a matter of which system is better, but rather how adept one is at arithmetic and how easy it is for that person to remember the main functional elements of a particular measurement system. Also, for one to believe that a particular system is better than the other simply because one is more comfortable with it is just silliness.
All of my rulers, power tools, and lumber yards use the Imperial system. If you want to pay to switch all of that over for me, go right ahead. Until then, I'll stick with Imperial.
USS_Ranger_Vet
Just for the record I wanted to make the correction that volume IS based upon the metre. One litre = 0.1m x 0.1m x 0.1m
I'm a Canadian and the metric system is a disaster in many ways. Everything in architecture for example is measured in mm. Room sizes, doors..... For example, no one knows how large is a room of 5375mm x 6135mm. "Is that 914mm door, 36 inches or 34, or am I getting confused with the 864mm door"?..... (Humans are best at imagining values between 1 and 20. Beyond about 20 and we relate the number to something we know. 45 feet? "Oh, that's about half the size of my property frontage." I could keep going but I'd be repeating what others have said. ...and don't get me going on the Celsius scale for temperature and its narrow range for human comfort.
Maybe if we'd started to use decimal inches, the metric agitators would have been satiated. 1'-3.6" (and one can easily graduate those 0.1" divisions into quarters to get even finer measurement. eg 3.625", 3.650", 3.675")
Much of the reason for metric agitation comes from "fraction phobia", which is just another way of admitting that mathematically, one is functionally illiterate.--public school level of math, ...or even less. As another commenter pointed out, his method is not the way in which someone fluent in math, would solve this fraction problem.
Yes, I do know that liquids are based on the same metrics. In fact, if everything was perfect, 1 litre of water weighs 1 kilogram. Thus, 1 millilitre of water = 1 gram. I didn't want to get into that as we were discussing linear measurement.
I have noticed that some measurements are expressed in millimeters or centimeters. But, it's not that difficult to think of the measurement in meters as you just move the decimal point. A room that is 5375mm x 6135mm is 5.375m x 6.135m, or, 5m 37.5cm x 6m 13.5cm.
It really doesn't matter which is the better system. We have 2 systems of measurement in the world. Although I'm an American and think entirely in imperial, I believe the metric system to be much better. The entire system is base 10, which is how we count and do math. I am tired of reading articles with measurements in them and then the roughly equivalent measurement in the other system. Most of the world uses metric, and so does the entire scientific world, and I believe we should convert to metric even if it has problems.
@Suburbanguy
+1 for decimal inches. They work great with micrometers (analog and digital), calipers, engraved rules, and CAD and modeling software. AND they have 3x higher precision than mm.
USS_Ranger_Vet
Have fun switching over. You won't believe the sudden jump in inflation that you'll experience. You'll pay the same price but instead of one U.S. quart, for example, you'll only get 1 litre. ....and because of everyone's confusion, manufacturers will use the opportunity to raise prices.
I believe that one of the reasons Canada moved to the metric system in the '70s was to obfuscate the high inflation of the time.
Learn from our mistake.
That's already happened. We haven't gotten a full quart of ice cream in years. They reduced the volume and kept charging us the same price. We all understand inflation. It's really despicable that they tried to hide it. BTW, I don't know if what we're getting is a litre or just less. Then there'd be the switch from gallons of gasoline to litres. Oh, what a mess that'd be. I'll stay with the imperial system. It's what I know and am comfortable with.
Ph.D. chemist by day and woodwork by night (well, mostly weekends).
All day, I work in metrics and it's fine I can visualize a gram or mg of material. Liters no problem.
The challenge for woodworking is that much past 10 cm, I can't visualize a measument. Also, I own all my tools and don't want to buy new ones. I could change and relearn and maybe get to that point for lengths, but I just don't see the point or need.
Also, as a woodworker, there is less measuring than some think. Maybe a bit more so as a handtool worker. Sure, for pieces you have lengths and widths for most. However, most of the measurements and done with a knife mark to fit and without ever knowing what it is. For dovetails, I just use dividers, etc.
@USS_Ranger_Vet
I'm can't really go into the mathematics of why 12 is a much more elegant base then 10 in a wood working forum. The reason metric uses 10 is because someone choose to use 10 not because everyone uses 10 fingers, there are many cultures with a traditional 12 counting system using the digits of the fingers to count to 12 in one hand and the other hand to count how many sets of 12. The Sumerians and Babylonians used a Sexagesimal (base 60) system! Your example of 12/3 = 4, 4/3 = 1.3333333 is a perfect example of why base 12 would be more elegant. In duodecimal 1/2, 1/3, 2/3, 1/4 and 3/4 have decimal equivalents of 0.6, 0.4, 0.8, 0.3, and 0.9, all nice short terminating sequences. 10 (this is 12 in base 10)/3 = 4, 4/3 = 1.4, 1.4 / 3 = 0.54. The two advantages of the metric system are unit conversion via simple decimal movement and that its easier for precision machines to work in decimal units rather then fractional units.
If one or the other system of measures were vastly superior, everyone would switch. Since that has not happened, I conclude that both systems have their merits.
I grew up with the metric system. It makes sense to me. I like using it.
For woodworking, centimeters are convenient base units, with millimeters expressed as decimals. For woodworking without something like a CNC machine, I see no reason to measure lengths less than 1mm, even though we often work to much tighter relative tolerances.
For me, the main problem is accurately reading imperial scales.
Pick up a ruler or tape measure with a good metric scale down to millimeters. I predict you will have no problem reading the millimeter scale regardless of whether you are measuring 1.1cm or 107.3cm. By "reading", I mean look at the scale and see 0.1, 0.3, or 0.7 centimeters without counting hash marks. A single prominent but unlabeled hash mark every 0.5cm makes this quite easy without much practice.
I am barely able to "read" a ruler with 1/8" markings. Certainly by the time I measure to 1/16", I generally resort to counting hash marks or carefully looking for the 1/2" and 1/4" marks and then working relative to those. Some scales label every few 1/16" (or some other fraction). These additional labels reduce the counting problem but often make it challenging to read and align the clutter of small labels with the intended hash mark. Imperial markings require much more of my attention than well-marked metric scales. I presume part of this is practice -- but I have acquired several decades of this practice.
I generally don't exchange measurements with others, so I have no problems working wood in metric measurements in the US. Many of my tools are in standard imperial sizes, like 1/8" saw blades, 3/4" router bits, or 5/32" drill bits but this seems of no real consequence to the way I work.
@user-3319453, I can see how it would be more difficult in Imperial if you used metric all your life. Of course, the same is true in reverse.
When I look at a metric scale, all the hash marks are the same height, except the halves and wholes. Now it's me who's doing the counting, constantly, because there's no obvious differentiation between the marks, except their position along the line.
The same is true if I purposely look at the very edge of a common Imperial 1/16 scale (Starrett comes to mind). But if I look at the tops of the marks, well suddenly there's a wealth of information - they're all different lengths, depending on the LCD. And depending which magnitude you're looking at, there are only one or two points to process, before coming to another 'landmark' representing a higher magnitude.
Confusing to articulate, easy to see in real time, if you're used to it. It's that mass of like hash marks that reduces me to counting on a metric scale.
In general, I think it's easier for the brain to process things in groups of three or less. Show me four or five little marks, all the same, and I probably need to count twice to be sure.
As I think about how to describe this, I'll admit it seems to rely on some facility with the various fractions, but to me (and I bet not just me) it's like knowing your multiplication tables. 12/16 = 3/4, without a thought.
I grew up from age 6 in New Zealand which was fully metric. I'm also a scientist so I think in metric. I live in the UK (Scotland) and got frustrated with my tape measure which had imperial measures along the top. So I sourced a metric only tape online and use that in the shop with an aluminium meter rule and a graduated large framing square.
I can of course work in fractions, I work out dilutions using ratios because they eliminate units, but decimals are much, much easier.
I work in both metric and imperial systems, and rather irreverently use them in combination when it suits. I realize though, when I start a project off in metric, I feel a sense of relief that my measurements are less likely to go wrong at some point down the line. So I have to admit that I much prefer metric over imperial, but referential measuring is even better!
The difference between the two systems was brought home to me with a thump back in 1970. I was a young chemical engineer in the paper industry. After several years working on newsprint machines in my home country of New Zealand, I joined a team in Sweden working on the computer control of paper machines. During my first visit to a Swedish machine, a colleague wanted to know the residence time of the pulp in a large rectangular tank in its basement. “Let’s see,” said another control engineer, “it’s about 4m by 10m and the average depth is around 4m. So that’s about 160 cubic meters, so 160 tonnes of water. The pulp concentration is usually around 3%, so that’s 4.8 tonnes of pulp, say 5 tonnes. She makes 20 tonnes of paper per hour so I guess that means the pulp is in there for around 15 mins.” It was almost as fast as he could talk. Imagine doing that in the imperial system!
The SI system created a problem for me though: back home I could walk down the 100 meters or so of paper machine scanning the control panels and gauges as I went. If anything was unusual or out of range, it stuck out immediately. But in Sweden I had to stop and convert each reading back to psi, Fahrenheit or whatever. I was as slow as a beginner. It took a long time to really come up to speed.
So I do have sympathy for those who think in Imperial. But please, get over it. You’re holding the rest of the world up!
user-7569054
No such thing as a tonne in the any metric system. Not in the SI, not in mks, not in cgs. It is a made up unit and is actually 1000kg which is a Mg.
In U.K. it is known as the long ton 2240lb as opposed to the short ton 2000lb. So Sweden hasn't gone metric. They've made up their own system (like here in Canada). (...and why do we buy meat and veggies in kg when they are actually weighed and not balanced?)
Fahrenheit is a terrible scale for human comfort. All comfort is squeezed into 10 Celsius degrees (between 20 and 30) In F scale, 60s is comfortable for getting outside work done. 70s better get it done in the morning. 80s? best to avoid heavy work but will need frequent water breaks. 90s is swimming weather. I don't even have to listen to the second digit. Home thermostats have to have half degree increments so that one can regulate the temperature properly. To use an arbitrary scale for human comfort where water freezes at 0 and boils at 100 is asinine and basically the height of technical illiteracy. "Oh, that's so easy to remember, zero and 100. Now if I can find a way to remember my name."
You were comfortable in the Imperial and now you're comfortable in the metric. See, makes no difference. Your attitude is one of contempt in suggesting that the rest of the world needs to "catch up". Most of the world's scientific development is coming from the U.S. and the Imperial system isn't holding them up. Most of the world needs to "catch up" technically with the U.S.
...and BTW One cubic foot weighs about 62 lbs. Standard knowledge (62.4) for a properly trained engineer. So I can estimate (use 60) just as well as those Swedes.
Retired P.Eng. (Canada)
You're quite right, I was brought up with the UK system where a ton was 2240 lb. I can see the superiority of the North American system.
Oh, and by the way: UK papermakers at that time used lbs/ream as a measure of the weight per unit area, as opposed to gm'sq m. Trouble was, although a ream was always 500 sheets, the size of those sheets varied depending on the grade of paper being produced. So I guess that was attitude forming too.
I was brought up on the British version of the imperial system in Australia, and then lived overseas in metric countries for fifteen years - I had to get really familiar with metric real quick. And I filled the car with litres.
Then I moved to England and found that if I bought a gallon of petrol I got 4.546 litres. Then I moved to Boston and found that a gallon of gasoline was only 3.785 litres. I still feel short changed on those American gallons. And a hundredweight was 100 pounds in USA and 112 pounds in the UK. There were lots of other variances in the "imperial system".
Then I returned to Australia which had gone metric in my absense, bought a pile of metric tools, and then inherited dad's imperial tools. Initially I tried to work in both systems and just got confused; ie I made silly mistakes, repeatedly. So I standardised on metric and ten years later got rid of all imperial tools so that they would not lead me astray.
The answer, in my case, was to use one system only, and stick to it.
Now, only three countries in the world are officially imperial - USA, Liberia and Myanmar - it will be interesting to see what happens over the next 20 or 50 years! Will USA be only imperial country?
a video is worth a ten thousand words :
https://www.youtube.com/watch?v=gV99abJ6YJo
THIRD SYTEM: There is actually a third system of measurement in common use around the world besides metric and imperial.
Navigation is traditionally done around the world in nautical miles. A nautical mile is defined as the length of one minute of latitude - remember 360 degrees to a circle, 60 minutes to a degree - and those measures are conveniently posted along the lefet and right hand margins of every paper chart. Metric countries all use nautical miles and measure speed in nautical miles per hour, called a knot in English. All have their own words for those measures. And a tenth of a nautical mile is called a cable. One nautical mile = 1.15 imperial miles = 1.85 kilometres = 6080 feet.
That last measure looks a little awkward, but it was not always so. A few hundred years ago the mariners measure system was:
* One minute of latitude = One nautical mile,
* Ten cables = One nautical mile,
* One hundred fathoms = one cable,
* Six feet = one fathom.
Thus a nautical mile was 1,000 fathoms - a metric number, or 6,000 feet.
Then it was realised that calculations of the Earths circumference were wrong, it was a little bigger, and the size of the nautical mile was increased to 6080 feet, or 1013.33 fathoms - nothing metric about that.
Perhaps an opportunity was lost?
user-533818
Sorry bud, but a nautical mile is actually one minute of longitude at the equator. (60 x 360 = 21,600 nautical miles at the equator.) I used to help my father when he taught celestial navigation. He'd have to have the exact answers to the homework that he assigned. We'd go to some pier on Lake Ontario--therefore knowing the altitude. He would shoot the sun for example, getting the exact angle above the horizon, while I recorded the exact time with the chronometer. We'd set the chronometer accurately from the Radio Canada time signal before we set out.
The first accurate marine chronometer was developed in Britain, which aided its exploration/colonization and strengthened the British Navy. The history of science is a fascinating subject.
I have found the easiest way to do fractions is with an app. I use "FractionCALC". You can add, subtract, multiply and divide just by the touch of the screen. No common denominator and it is free. If I am working using fractions a lot I just have my phone on the workbench like any other tool...........
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