Why are English units so confusing?

[SW VandeCarr]

When are you yanks going to stop calling them 'English' units? We stopped using imperial measures ages ago, don't blame us!

Yes, but they are still historically English. If we called them "American"' units, you'd probably complain about that too.

Actually, I don't know why the US kept them as "customary units." After the revolution, the Americans wanted to distinguish themselves from everything British including the language and the way a fork is used at meals. The latter was successful, but not the former (well, maybe partially successful). Serious consideration was given to adopting German as the national language.

Given that the metric system was a product of the French Revolution, I would have thought the US would have embraced it. However, Americans like their freedoms and have a broad interpretation of the First Amendment. The government has a hard time forcing people to conform to any kind of expression. The US doesn't even have an official national language.

 

[Integral]

You will have pry my foot/inch tape measure from dying hands. For the reasons Phrak has already explained, there is no way I will never own or do I want to use a metric tape.

Need I point out that upon conversion to binary .1 becomes something less then nice. Where as the common subdivisions of the inch are perfect binary numbers.


Down with .1!

 

[TubbaBlubba]

I cannot see attempting to define the basic unit of length as 1/10,000 the distance from equator to pole as anything but the result of arrogant disregard. (Uncle Marx would have been proud.) Beware of that trap.

Defining it as the foot of an English king is clearly the superior method.

 

[Chi Meson]

You will have pry my foot/inch tape measure from dying hands. For the reasons Phrak has already explained, there is no way I will never own or do I want to use a metric tape.

Need I point out that upon conversion to binary .1 becomes something less then nice. Where as the common subdivisions of the inch are perfect binary numbers. Down with .1!

You do know that the inch is defined as 2.54 cm, right?

My favorite tape measure has both inch and cm. I think that having been a bike mechanic and then a physics teacher has made me literate in both sets of units.

I usually tell my students that a meter is "the same as a yard," if you're just thinking about it. If you're actually buiding a jet, you'll need to be a little more specific.

And take any speed in m/s, double the number to get mph. That won't hold up in court, but when was the last time you said "That guy was going about 82.7 miles per hour" ?

 

[lisab]

At my work we have a test that requires use of a ruler that is in inches, with 1/10 hatch marks. A metric English ruler .

 

[TubbaBlubba]

At my work we have a test that requires use of a ruler that is in inches, with 1/10 hatch marks. A metric English ruler .

There's got to be a law against that.

 

[SW VandeCarr]

At my work we have a test that requires use of a ruler that is in inches, with 1/10 hatch marks. A metric English ruler .

NOAA reports rain and snow in decimal factions of an inch.

 

[Moonbear]

I seem to like using the metric system for small things and the English system for big things. For example, once you get smaller than a half inch, I start switching to using millimeters. But for larger things, feet, yards and miles makes more sense to me than decimeters, meters and kilometers.

Same with weight. I buy produce and meat by the quarter pound, half pound, pound, but smaller quantities I prefer thinking about in grams rather than ounces.

Volumes present a bit of a problem, because common recipes are written with teaspoons and tablespoons in mind, but really, without having an actual measuring spoon, I really can't comfortably guesstimate volume using those measures. Cups, pints, quarts, gallons, sure, those all work for me. But small volumes, I would be much more comfortable measuring in milliliters.

 

[Chi Meson]

At my work we have a test that requires use of a ruler that is in inches, with 1/10 hatch marks. A metric English ruler .

Isn't that an "Engineer's" rule, as opposed to an "architect's" rule? I know places like Pratt & Whitney use decimal inches as their base unit. That way it takes only a 2.54 exact conversion to make everything metric.

 

[Proton Soup]

Isn't that an "Engineer's" rule, as opposed to an "architect's" rule? I know places like Pratt & Whitney use decimal inches as their base unit. That way it takes only a 2.54 exact conversion to make everything metric.

when i took engineering drafting many moons ago, we had something similar called "scales". but naturally, most were not on a 1:1 scale.

 

[Redbelly98]

At my work we have a test that requires use of a ruler that is in inches, with 1/10 hatch marks. A metric English ruler .

American-made milling machines and vernier calipers typically use decimal inches, in 0.001" gradations.

 

[Phrak]

Isn't that an "Engineer's" rule, as opposed to an "architect's" rule? I know places like Pratt & Whitney use decimal inches as their base unit. That way it takes only a 2.54 exact conversion to make everything metric.

A machinist's steel rule is called a scale. It might be what you're thinking about. They range in length from 6 inches to a few feet. Some are stamped or etched in both metric units and inches. If only inches, you get hash marks every 0.1" and 0.01" along each edge. On the other side are fractions with resolutions of 1/32nds and 1/64ths.

 

[lisab]

A machinist's steel rule is called a scale. It might be what you're thinking about. They range in length from 6 inches to a few feet. Some are stamped or etched in both metric units and inches. If only inches, you get hash marks every 0.1" and 0.01" along each edge. On the other side are fractions with resolutions of 1/32nds and 1/64ths.

That must be it. It's a steel rule 6" long with 0.1" along one edge...hmm, don't think I've ever looked at it closely enough to remember what's on the other side. I'll check it out tomorrow morning.

 

[Chi Meson]

when i took engineering drafting many moons ago, we had something similar called "scales". but naturally, most were not on a 1:1 scale.

That's right, a "scale." I have several neat triangular scales, some of them in decimal inches, one "Architect's" which is 1/12ths divisions (scaled-down feet and inches), and some in 1/16ths. All this from my fathers before me.

My father, g'father, and g'g'grandgather were all engineers. My g'g'grandfather actually was a railroad engineer, back when engineers were engineers.

 

[SW VandeCarr]

How about a 'scientific' system based on powers of 2 and three basic units: inches, pints and pounds. A pound could be defined as the weight of 1 pint of pure water (pretty close to the current US pound)

The notation could be nU|log_2 where n is a positive real number and U is a unit.

So 3 pints would be written 3 p|0, just 3 p or 1.5 p|1; a gallon: 1 p|3.

A quarter pound would be 1 lb|-2.

For distance, one mile can be closely approximated by 1 in|16 =1.034 mi.

Or we can just forget it and be quaint.

 

[mgb_phys]

Yes, but they are still historically English. If we called them "American"' units, you'd probably complain about that too.

At least it annoys the Scots - that's the main thing.

I don't know why the US kept them as "customary units." After the revolution, the Americans wanted to distinguish themselves from everything British ...
Given that the metric system was a product of the French Revolution, I would have thought the US would have embraced it.

It was considered by the more scientifically minded founding fathers (imagine a senior politician with any sort of scientific reputation!) but the engineers were all British and the main industrial trade was with Britain so it was impractical to do anything else. Then when the railways 50years later arrived they used British engines and parts.

Actually for most of the 19C engineering in continental europe was often in Imperial simply because Britain manufactured so much of the machine tools and parts. A little like how electronics is now done in fractions of an inch because of early US dominance in ICs.

 

[SW VandeCarr]

At least it annoys the Scots - that's the main thing.

It was considered by the more scientifically minded founding fathers (imagine a senior politician with any sort of scientific reputation!) but the engineers were all British and the main industrial trade was with Britain so it was impractical to do anything else. Then when the railways 50years later arrived they used British engines and parts.

Actually for most of the 19C engineering in continental europe was often in Imperial simply because Britain manufactured so much of the machine tools and parts. A little like how electronics is now done in fractions of an inch because of early US dominance in ICs.

Interesting. So the US was dependent on Britain for manufactured goods, and Britain was dependent on the US for cheap high quality cotton. Good argument for inches, pints, pounds and slave labor (or is it labour?).

 

[Moonbear]

At my work we have a test that requires use of a ruler that is in inches, with 1/10 hatch marks. A metric English ruler .

That makes as much sense as any other unit of measure. The nice thing about the English units is that the base unit generally has some practical meaning. It's the fractions of units that get weird dealing with 1/2, 1/4...1/32, 1/64 of an inch gets weird. But if you take the base unit, an inch, and then subdivide it by decimals, it's really the best of both worlds, and really no more arbitrary than using a centimeter as your base unit.

 

[Phrak]

How about a 'scientific' system based on powers of 2 and three basic units: inches, pints and pounds. A pound could be defined as the weight of 1 pint of pure water (pretty close to the current US pound)

The notation could be nU|log 2 where n is a positive real number and U is a unit.

So 3 pints would be written 3 p|0, just 3 p or 1.5 p|1; a gallon: 1 p|3.

A quarter pound would be 1 lb|-2.

For distance, one mile can be closely approximated by 1 in|16 =1.034 mi.

Or we can just forget it and be quaint.

But at this point the astronomers should be feeling unfairly left out. Without much change to your program we could redefine the second as the time it takes light to travel one parsec, and the distance, 3.26 light years, would be the new meter. One solar mass would be the new gram. One teaspoon would be the volume occupied, not by one gram of water, but one gram of neutron star matter. It would only make sense with so little water found in space.

 

[SW VandeCarr]

12 inches in a foot, 5280 feet in a mile... binary?

Actually, 5280 ft is not arbitrary. A square mile is 640 acres which can quartered into 160, 40 and 10 acre units. The 10 acre unit is divided into ten equal strips of 1 acre each (exactly one eighth mile long and 1/80 mile or 66 ft wide). Strips are obviously more practical for plowing.

The foot isn't binary, but it's divisible into half, quarters, thirds and sixths by whole numbers of inches.

 

[Jack21222]

Actually, 5280 ft is not arbitrary. A square mile is 640 acres which can quartered into 160, 40 and 10 acre units. The 10 acre unit is divided into ten equal strips of 1 acre each (exactly one eighth of mile long and 1/80 of mile or 66 ft wide). Strips are obviously more practical for plowing.

The foot isn't binary, but it's divisible into half, quarters, thirds and sixths by whole numbers of inches.

I didn't say arbitrary, I said binary. The poster I quoted was extolling the virtues of a binary system, where it goes 1/2, 1/4, 1/8, 1/16, etc.

 

[SW VandeCarr]

I didn't say arbitrary, I said binary. The poster I quoted was extolling the virtues of a binary system, where it goes 1/2, 1/4, 1/8, 1/16, etc.

I did say arbitrary, but I could have also said binary. Quarter sections are 1/2 mile square, quarter-quarter sections are 1/4 mile square, "thrice" quartered sections are 1/8 mile square (consisting of 160, 40 and 10 acres respectively).

A foot is divisible into halves and quarters by whole numbers of inches.

It's quaint, but it serves a purpose.

 

[Phrak]

No one yet has brought up the progressive radix system where successive digits change basis. The most straightforward is the simple progression 1,2,3,4,5,6 and so on. This has the advantage in that 7!, for instance, is expressed as 1000000.

 

[SW VandeCarr]

No one yet has brought up the progressive radix system where successive digits change basis.

Are you surprised? How would you write 101/256ths of a hogshead of American beer in a progressive radix system?

 

[Phrak]

Are you surprised? How would you write 101/256ths of a hogshead of American beer in a progressive radix system?

I'm glad you brought this up. It's the same thing I've been asking myself, although I wasn't thinking in hogsheads.

Fractions less than one would be the summation

0 + A/2! + B/3! + C/4! + D/5! + E/6! + F/7! + G/8!... or

0 + A/2 + B/(2*3) + C/(8*3) + D/(8*3*5) + E(16*9*5) + F/(16*9*5*7) + G/(128*9*5*7)+ ...

I'll use the notation 0.A.B.C.D.E.F... to represent the fraction. Already we can see that a number such as 21/24ths can be represented in a rich number of ways: 0.0.5.1, 0.0.4.7, 0.0.3.13, and etc. And so your hogshead count would be 0.0.0.0.0.0.31815 using one possibility. It's not very interesting, and the digits are still in decimal. But, later, on that.

With a mind toward economy, a modification should be in order. It should be much more efficient to use a modified sum of fractions:

0 + A/2! + B/(2!3!) + C/(2!3!4!) + D/(2!3!4!5!) + E/(2!3!4!5!6!) + ...

0 + A/2 + B/(4*3) + C/(32*9) + D/(1024*81*5) + ...

101/256 = (1+4+32+64)/256 so the new and improved representation would be 0.0.4.9.6480.

1/3 would be 0.0.4. But what is more interesting; can any rational number be expressed as a finite string of numbers separated by radii?