Why are English units so confusing?

[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?