Measurement Systems

On Metric and Imperial

part of a 20cm stainless steel workshop ruler
part of a 20cm stainless steel workshop ruler

A puzzle to start with.

Given these numbers:

1   4   5   16   3   8   7   …

What is the next one in the sequence?

The answer can be found later on this page.

Debates about the metric system have not died out.  At least there is now only one serious system in use, with unfortunately one large bloc still sticking to the everyday use of an older one.  Here I attempt to look at the many facets of the “problem”.

Origins

There were many systems of measurement, both over time and certainly over space.  Administering an empire or country means accounting, and that means ways of comparing things, which needs a measurement system.

Certainly I'm not going to even try to list systems that existed in the past:  there are too many.  They differed between geographically and/or economically distinct areas, and inside the same area of the same country between trades:  a jeweller did not use the same weights as the grocer next door.

The older systems are still of historic and sociological interest.  You can find numerous documents about them.

Rough measurement sytems may have existed before writing.  Counting most certainly did:  comparing the number of sheep in the flock that went to the pastures in the morning with the one that came back in the evening was certainly done.  Counting is a form of measuring, especially if the objects counted are all reasonably the same, such as sheep or the seeds of certain plants.

More advanced societies with written records needed systems of measurement:  attributing and dividing land area, weighing goods in trade transactions, designing large permanent buildings.

Geometry was more important than actual units:  Stonehenge and the pyramids can be built by geometry alone, without deciding on units.  But as soon as there is some economic factor involved, one needs a contract between people and something to guarantee the fairness of the transactions.  An agreed and certified system of measures is important.

Certifying needs standards against which to compare.  The most obvious measures are the length units related to the human body:  yard, foot, inch. It is more problematic for weights and volumes, but even lengths differ greatly between adults, so it was not surprising that the body of the monarch provided the lengths that one could trust.

Except when changing monarchs.

Facets of choosing units

Constancy

The problem of modifying units when changing monarchs shows that it is important to have standard units that are independent of the whims of human societies, in time and place.  Somewhere there needs to be a standard foot, a standard pound, etc.

Reproducibility

Ideally a standard unit should be producible locally, without having to travel to a shrine to compare it with the single agreed upon object that is kept there.  For example, one can define the unit of time as a fraction of the daily revolution of the Earth, and that can be accurately observed anywhere.

Practicality

Units should be easy to apply:  they should correspond roughly to amounts that are of everyday use.

There must also be different magnitudes:  one needs miles to express travel distances but millimetres to work in cabinet making;  grams in the kitchen and tons on the building site.

Psychological acceptance

It's no use to the general public if the units are obscure.  Physicists will tell you that anything with units is of no importance in physics and they will happily make the speed of light equal to 1 because that makes the mathematics simpler.

But people need nice “round” units like pounds and gallons, metres and minutes.  Things that are easy to get a “feeling” for, and remember.

Computability

It must be possible to calculate easily within the system.  Calculations are important in planning and assessing.  Engineers, contractors, surveyors, manufacturers, all need to be able to make precise calculations but also quick estimates by mental calculation.

Let's tackle calculation first.

Number Systems and Calculating

Bases

The number system you are most familiar with has 10 as its base and it is a positional system.

This has two important consequences:

There are a few other bases sometimes colloquially used:

(I did not mention binary because it is almost never used in social contexts)

Quirky?

Languages deal with numbers in some strange, quirky ways:

In English the numbers between ten and twenty have a weird, irregular syntax:

… ten, eleven, twelve, thirteen, … nineteen, twenty, twenty-one, … twenty-nine

A regular syntax would be:

… ten, ten-one, ten-two, ten-three, …

and twenty would have to be two-ty to be regular like six-ty.

English is not the worst offender, (proper) French has some really bad ways:

99 = quatre-vingt-dix-neuf = 4×20+10+9

In a doctor's waiting room in France I once heard a mother teaching her little daughter to count.  The kid went:

… quarante-sept (47), quarante-huit (48), quarante-neuf (49), quarante-dix (40+10), …

whereupon the mother instantly corrected:

NON! Cinquante! (50)

But I grinned and said:

Mais elle a raison:  on dit bien soixante-dix (60+10) et pas septante (70), pourquoi pas quarante-dix au lieu de cinquante?.

(“But she is right:  one says sixty-ten not seventy, so why not forty-ten instead of fifty?”)

I don't think the mother was pleased. But in neighbouring Switzerland one does indeed say septante and nonante, much simpler and more regular.  Using multiples of 20 is a remnant of past ages, and it has survived even in French only for the numbers 60 and 80.

German and Dutch have kept the early positional system whereby the units come first and the multiples of ten later:

25 = fünf-und-zwanzig =  vijfentwintig = 5 + 20

(by the way:  we got the habit of starting with the most important digit from misinterpreting the Arabic texts, written right-to-left, that brought the positional system to Europe; Arabic also started with the least important position)

One last thing about mixing up / messing up positional number notation:  why do some people use month-day-year instead of day-month-year?

Calculating

We all use base ten in calculations, and so do our calculators:

a typical computer screen calculator
a typical computer screen calculator

Moreover, we calculate with decimals, not with fractions.  Fractions are out, except perhaps for very simple ones like 1/2, 1/3, 3/4. We write 3.1416 not 22/7.

Engineering Multiples

Three digits is the preferred grouping in writing:  we write 1'000'000 to denote one million, because our brains cannot quickly perceive groups of more than three things at a time (though some people can deal with four, it is not common).

These groups of three have been used in engineering for a long time to deal with the large ranges of numbers encountered there.  Prefixes are used to keep it concise:  engineers talk about kilovolts = 1'000V = 1kV, milliamps = 0.001A = 1mA and so on.

We have become used to these factors of three digits, especially since computing has permeated all activities. We are familiar with the prefixes milli, kilo, mega, giga and tera.  They are even used in finance now, where the price of a house may be expressed in k€.

Although there are words for 10× and 100×, we do not use them anymore.  We do not say “a decametre” or “a hectometre” but “ten metres” or “a hundred metres”.

The Metric System

The metric system had two main goals:

The first point meant going out to Nature, linking the units to objects and materials found there, that were accessible to everyone anywhere on the planet.

The most important units are those for length, mass (often confused with weight), and time.  There was very little knowledge about electricity, so that was included much later.

Length

At the time length was measured in inch, feet and yards for small distances, with each of these units having a local value and a local name (zoll, pouce, duim, inch; fuss, pied, voet, foot; el, yard, …).  Longer distances were in miles of some kind (meil, mille, mijl, mile).

A good object for deriving the distance unit was the Earth:  we are all on it and can measure the circumference from astronomical observations combined with an arbitrary local distance unit.  Thus a standard distance unit can be calculated anywhere on the planet by someone with a telescope and their local yardstick, it suffices to specify how it is to be done.

There were several miles in use, the most useful in navigation and surveying being the nautical mile.

A nautical mile is the length on the surface of the sea that corresponds to a difference of one minute of arc:  the full circumference is divided into 360 degrees, each degree into 60 minutes. There are therefore 360×60 = 21'600 minutes which means it's 21'600 nautical miles to circumnavigate the planet.

right angle = 90º 1º = 60 arc minutes 1 minute of arc = 1 nautical mile
the nautical mile

The metric system uses 10, not 60 or 30 or 360, therefore it divided the right angle into 100 grades, or the circumference into 400 grades, which is sufficiently close to 360 so that it should not have upset anyone. Every grade is further divided into 100 minutes.

That makes 40'000 minutes to go around, and a “new” nautical mile of 1kilometre. The kilometer was then divided into 1000 to get to the metre.

right angle = 100 grades grade = 100 arc minutes 1 minute of arc = 1 kilometre
the kilometre

the kilometre is the metric equivalent of the nautical mile

Length derived units

From length one can immediately derive area and volume units:  the square metre and the cubic metre.

But the cubic metre is too large for household use.  It was diveded up in a thousand litres. A litre therefore is also the volume of a cube of 10cm at a side. That is a convenient size, though in production it is usually not presented in the shape of a cube but as a brick.

Mass

Mass needed a substance easy to find everywhere:  water was a good choice.

Thus the kilogram of mass was defined as the mass of a litre of water.  That has a problem, because water's density changes with temperature.  The final kilogram was made as a cylinder of platinum and iridium, corresponding to the mass of a litre of water at its densest (4ºC). That standard itself has since been replaced by a different implementation.  The kilogram was the last metric unit to get a definition in terms of fundamental physical quantities.

Time

The unit of time was the length of the daily rotation of the Earth.  Classically this is divided into 24 hours, each hour into 60 minutes and each minute into 60 seconds.  The metric system used 10 hours, 100 minutes and 100 seconds, which makes the metric second a little shorter than the familiar second.

BUT… this second was never adopted, the old classic second remained in use instead! Therefore at least one base unit of the metric system does not correspond to the decimalisation idea!

Angle

In order to obey the rule of decimalisation, angles should not use 90º, 60 minutes, 60 seconds;  they should use 100 grades, 100 minutes, 100 seconds. But this again was not adopted and we continue to measure angles in the classic degrees.

Classic degrees introduce a difficulty in mental arithmetic for aeronautical navigation:  one has to add/subtract 180, often under time constraints, instead of the much simpler 200.

Temperature

The freezing point and boiling point of water are the two defining points of the metric temperature scale:  they define 0ºC and 100ºC respectively.  (note: boiling has to happen at sea level, so it is also dependent on the average atmospheric pressure, and is therefore scientifically not a good choice, but it is an easy point to remember).

The rule of decimalisation

Using base 10 and no other factors than 1 everywhere was actually proposed a few times before the metric system (see the web) but never adopted.

More half-metric units

The unit of time is not a division by power of 10 of the day, we have no metric clocks.  But it's not the only weird unit.

The calorie is not metric:  it is the amount of energy needed to heat a cubic centimetre by 1 degree Celsius.  That sounds all very metric, but it is not:  the metric unit of energy is the Joule.  The calorie depends on the specific heat of water.

A Joule is the energy needed to displace a force of 1 Newton by 1 metre, and a Newton is the force necessary to accelerate a mass of 1kg by 1 metre per second, per second.  A calorie is 4.1868 Joules.  A bad factor.

Food used to be labelled with its calorie content, but Joules are replacing that:

Energy content label
energy content label on yoghurt:  320kJ per 100gram
(an adult needs around 7000kJ per day)

A kilo-Watt-hour (kWh) is not metric.  Again it sounds like that, but an hour is 3600 seconds. Therefore a kWh is 3'600'000 Joules, not a good factor.

Speed is measured in km/h instead of metres per second.  100km/h is 27.777 metres per second, a bad factor.  The metre per second would have been perfectly useful:  1m/s is 3.6km/h or walking speed (talk about getting the human factor in!)  10m/s to 15m/s is a reasonable speed in town and 30m/s would indeed be reserved for open roads and motorways.

But would it give us an idea how much distance we can cover in an hour?  Not unless we also change the clock, but then the second changes as well,  Do this calculation for your own pleasure (answers at the end of the page).

A metric horsepower is defined as the power necessary to lift 75kg 1 metre per second. That is 735.75 Watt.  It is close to the Imperial horsepower, but it is certainly not a metric unit, firstly because of the strange 75kg but also because it concerns a force by weight, hence involves the acceleration of gravity, 9.81m/s2, two bad factors in a single unit!

We often use kg for force instread of Newtons.  The kg force is not useful in engineering calculations for strengths of constructions.  There is a steel access panel in the road just outside my house:

an access panel in the road
an access panel in the road

It shows the maximum load admissible as 250kN. That is metric indeed.  It corresponds roughly to the force exterted by the weight of a mass of 25 tons.  Obviously the truck driver knows how much mass is in their truck, but not the force that exerts on the panel and it is unlikely that they know one has to multiply by 9.81m/s2.  Fortunately that happens to be a factor of approximately 10, so all they need to do is divide the indication on the panel by 10 to compare it with the mass of the truck.  But not funny.

Real stupidity

Or is it just the very evil power of tradition?  Many light bulbs are still sold with a rating in Watt, which was always wrong and is not even helpful these days as there are varieties of technologies:  LED, incandescent, fluorescent.  Light output should always be given in lumen:  that is the measure of light perceived by the human eye.  Watt is a measure of power consumption, it gives no idea about how much light comes out because that varies more than tenfold depending on the technology used. Here are some packaged bulbs observed at a supermarket, with good and bad labels:

light bulb
light bulb with the label in Watt and no lumen indication
light bulb
light bulb with the label in lumen (806) but still giving incandescent equivalent (60W)
light bulb
light bulb with the label in lumen (580) and also its actual consumption (7W)

This last one must be quite good:  it is dimmable and has 15 years lifetime.

As a rule of thumb one can say that LED bulbs will give around 100 lumen per Watt (90lumen/W is closer but more difficult to use).  Our living room, which is rather large, needs between 3000 and 5000 lumen for comfortable lighting.

See chapter psychological stuff for why the wrong unit of Watt is still used.

The Imperial System

This system is now only used in the USA (and a few minuscule nations such as the Bahamas, Belize, the Cayman Islands and Palau).

Apology of the Imperial system

The main argument cited by its supporters is that it is more “human” because some of its units are related to the human body.  This is perhaps true for some length units such as inch, foot and yard, or even the (statute) mile, but certainly not for others.

How does a pound relate to the body?  A gallon?  How does anything electric relate to the human body?

But not only are the units quite arbitrary, the relation between them requires numerous factors that are not 1 or powers of 10.  Some are outright weird and difficult to remember.  Just a few examples:

Then there is the question of how to reproduce these units without recourse to artifacts.

One possible advantage

Observe that many of the factors in the list above are powers of 2 and some factors are divisible by 3.

The base 10 of the metric system is only divisible by 2 and 5.

Other Quirks

There are at least two different miles in use:  the statue mile (1.609km) and the nautical mile (1.852km), with no common factor at all.

There are US and UK gallons, troy ounces, long and short tons, and so on.

Temperature is interesting:  here are the Fahrenheit and Celsius scales compared:

ºF -40 -30 -20 -10  0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 ºC -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 water freezes water boils body core room temp. (mighty cold)
two temperature scales

Celsius is really simple:  water freezes at 0º, useful before talking a walk outside in winter;  water boils at 100º, also something you witness often.  Then the only thing to memorise is: 37.2º which is your body temperature if you have no fever. If you are young and active then room temperature is 20º, but as you get older you will probably like it somewhat warmer, maybe up to 25º.

I'm sorry but I can't see any logic to the Fahrenheit scale.  0ºF is "cold brine", perhaps it's when the sea freezes, but that's hardly an everyday experience.  100ºF is close to the human body temperature, but it's not exactly right.

Obviously, if you have spent a long time learning it by heart, then you will be familiar with the Fahrenheit scale, but it does not take an effort to adapt to the Celsius scale, as long as you don't try to convert back to Fahrenheit.  Just learn those four points:  ice, room, fever, boil.

Current Definitions

All Imperial units have now been defined in terms of the metric system.  For example the inch is defined as 25.4mm.

Obviously all electrical units were taken lock stock and barrel from the metric system.

Conversion Conundrum

A friend recently wrote to me:  “a pint of beer still sounds far more appetizing to me than 0.47 litres of the same”.  That was jokingly, but the point is well taken:  there is a problem of converting from one into the other.

For daily use, the amounts of anything must be “round numbers”.  And a pint is “round” in Imperial, but not when converted to metric.  Likewise a litre is round in metric but comes to 2.1133764 pints in imperial.  Not appetizing indeed.

When one discusses conversion to another system, it really means producing goods in quantities that are “round” in that system. This is a door in my house:

a standard metric door
a standard metric door

It came straight off the shelf:  it is 2.0m high and 90cm wide.  Doors are fabricated in widths of 100cm (entrance), 90 (indoor standard), 80 (indoor small), 70cm (indoor narrow).  Those are useful and pleasing dimensions and they work very well.

Likewise, the circuit breaker box protecting our sockets from overload, has breakers rated in round numbers of Ampères:  usually 10A, 16A or 20A.

electric circuit breaker box
electric circuit breaker box

When we go shopping, fluids are packaged into containers of whole litres:

a litre of soup
a litre of soup

But it is not always the case:

a can of conservew
a can of …  (OK, made in England)

The problem with base 10

Using base ten is a historic accident. The accident took place 350 million years ago, at the transition from the Devonian to the Carboniferous, which was accompanied by a great extinction.  Nearly all land vertebrates died, of the survivors all happened to have five fingers.  Nothing left with four or six or eight.  Around that time is a span of about 15 million years where the fossil record is still problematic, and this period has been given the name of its discoverer:  “Romer's gap”.

The important point is that because of this accident we have five fingers on each hand, not six or four or eight.  Thus we count on ten fingers, whence the popularity of base 10.

our hands
our hands

Had the accident preserved animals with six fingers and we were descended from them, we might now be using base 12.

Advantages of base 12

When was the last time you cut up a pizza into 10 parts?  Or have you ever tried to tile the floor with pentagons instead of hexagons?

tiling a floor
tiling a floor

The problem with base ten is that it is not divisible by three.  It is also not divisible by four.

Both three and four are very useful in everyday life.  Tables, rooms, sheets of paper, have four sides;  chairs have four legs not five.

Dividing or multiplying by two is a basic change in size; often four is even better.  Three is the next prime number after two, not five.  Two-by-three is a small, handy rectangle of objects, two-by-five is not.

Base 12 has divisors 2,3,4 and 6. It is a much more practical base than 10.

You can buy eggs (just about) in boxes of 10.  But 20, being 4×5, is more convenient, as is the usual 6.  Wine and beer are packed by 6, not 5, which would simply not work, nor 10 which would be too many.

Eggs
Eggs
Eggs
or eggs

A better base then would have been 12, but 10 is what we're used to.  If you are interested, there are groups actively proposing a change to a duodecimal system.

Psychological stuff

Some years ago I had a discussion with my sister-in-law.  Being born in England just before World War II, she was initially brought up in the Imperial system but then switched to metric/decimal.  She now lives “on the continent”, so she does everything in metric. But she told me that the biggest problem she had with converting to metric was that suddenly she no longer had “pegs to hang things on”.

That was an interesting remark, and she meant this:

pegs to hang things on
pegs to hang things on

To her, and I fully sympathise, certain units were associated with certain circumstances.  In the metric system one does not have these associations in the same way as in the Imperial system, and I had never heard the effect mentioned, nor have I heard about it since.

So she thought of pounds and pints and inches as associated with, for example, the kitchen;  whereas tons and miles and yards were used elsewhere, outdside.

As the metric system emphasises the ease of converting from kilometres to metres to millimetres, she was confused and missed her “pegs”.

I had never thought about it, but it is obviously true:  one does not use kilometers and tons around the house, and one never needs millilitres on the road.

Different orders of magnitude are not used in the same circumstances.

The ease of conversion provided by the factors of 10 does not help much in day-to-day usage.

Having 1760 yards to a mile is indeed an awkward factor, but except in engineering and science, that awkwardness does not matter much:  objects measured in yards hang from a different peg than those measured in miles.

Five Reasons why Imperial Measures hang on

We can now ask why the Imperial system still hangs on.

Firstly, it is only in the USA really, and that is a geographically fairly isolated political bloc, highly integrated.  For example, changing could not be done by successive conversion state by state from East to West over a period of time.  But it would also not bring immediate benefits in commerce because there is very little day-to-day exchange with neighbouring countries.  By contrast, a small country like Switzerland could not afford to use a system different from its immediate neighbours:  people go across the borders in both directions all the time.  It's enough of a nuisance to have to use two different currencies (Swiss francs and Euros), it would be hell if measurements were also different.

For what they are worth, here are my five reasons for why Imperial still hangs on in the USA:

Divisors

As mentioned earlier:  daily use often requires division by 2, 3, 4 and base ten has only 2 and 5, whereby 5 is almost useless.

The only redeeming quality for the decimalisation rule is that we all know well how to calculate in base ten:  I remember vividly a time when I was in the US, and needed to divide a piece of paper into three columns. There was only a ruler marked in inches.  But such rulers show inch divisions in factors of 2 only.  I could measure the width of the paper, 8.5 inch, and I could divide that by 3:  2.833 inch.  But where was 2.833 on the ruler? There were no tenths of an inch, only eights.

Pegs in your brain

Again as mentioned earlier, one does not often need to convert from one order of magnitude to another.  The usage of certain units in certain conditions is very familiar.

In addition, one almost never needs to go from one type to another.  You do not need to know the relation of the kilogram to the metre: the coherence argument, while very important, is almost never used by ordinary people in their daily lives.

Just to clarify what we talk about:  suppose we want to be sure that the floor will support the new jacuzzi.  The jacuzzi being 2×2m and filled with water to 0.5m deep, it is “obvious” that it holds 20×20×5=2000 litres, and because a litre of water by definition is 1kg, we have two tons of water to support.  This is not easy to calculate in Imperial measures, but then again, how often does one need this type of information, and which percentage of the general population would be able to calculate it in the first place?

It's in the language

The old units are built into the language:

It is not just the expressions:  the terms are also much shorter, monosyllabic.  “Inch” is easier to pronounce and write than “centimetre”.  I think this is mainly limited to the English language, other languages do not have similar expressions.

Move Posts

Round numbers are important. Consider this panel on a Scottish motorway:

panels along the road
panels along the road

That's 9 miles.  Or 14.84km.  If you converted that, you woudl like to see “Edinburgh 15km”, not 14.85.  But then you would have to move the panel by 160m.  Of course, in this particular case, the city is large so you could leave the panel where it is and paint 15km on it, it's only a small error.  It would not work in many cases though, and it's not just road panels that would need adjusting.

USA

The case of the US economy is more interesting.

Obvously all factories would have to re-tool.  They would need to produce bottles, boxes, cans in dimensions that would be round numbers in metric units.

The argument advanced here is that it would be an inordinate cost.

I'm not certain that is really valid:  any new production run requires re-tooling anyway.

Plus that often there are dimensional adaptations to avoid price changes:  you may have noticed that for many consumer goods the price does not go up, but the quantity you get is somewhat less.  Chocolate bars used to be 50g, then they were 49g and now I've seen 47.5g.  Clearly it is less expensive to re-tool than to lose consumers because of a price hike.

A Dream

The Imperial system is difficult to work with:  it is incoherent and full of strange factors.  It is not in any significant way linked to human nature.

The metric system has some minor inconsistencies, but its ideas are sound.

The major problem is the use of base 10 for calculating.  Could we make an entirely new system, using base 12?  It would be coherent like the metric system, but have factors 2, 3, and 4, like much of the Imperial system.

The occasion could be used to change the names of the units too:  use monosyllabic ones.

Duodecimal Numbers

Counting in twelves instead of tens would need two more digits.  Let's call them dix and elf:

twelve digit signs
twelve digit signs

There should be a proper competition for the shapes of the two new digits, I just invented two of my own in the figur above.  While we're at it, we might take the opportunity to change the zero and one so that their new shapes would not be so close to the shapes of the letters O and I and l, which leads to confusion now.

You would then write a dozen as 10 and a gross as 100. But you could easily divide by 3:  10/3=4.

Puzzle Answer

Here is the answer to the puzzle posed at the start of the page:

16

Consider a set of spanners using Imperial measures:

a set of spanners
a set of spanners

The size of their corresponding nuts goes up in 1/16th of an inch.  The labels on the spanners should read:

4/16 5/16 6/16 7/16 8/16 9/16 10/16 11/16 12/16 13/16 14/16 15/16 16/16

But somehow there is an abhorrence of fractions that are not reduced.

Instead of going 4, 5, 6, 7, 8, …  all in 16ths, the 4/16 is reduced to 1/4, the 5/16 can't be reduced, the 6/16 becomes 3/8, 7/16 can't be reduced, 8/16 becomes 1/2, etc. and the labels really are:

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16 1

Reading the sequence of numbers without the dividing lines gives you 1, 4, 5, 16, 3, 8, 7, 16, 1, 2, …

This sequence of labels on spanners is to me horribly complicated to work with:  what is the next bigger size spanner after 3/4?

In contrast, metric spanners just go 6, 7, 8, 9, … mm:

metric spanners
metric spanners (my own old and battered set)

An interesting object

Many years ago a colleague of mine cleared out his workshop and gave me a spare micrometer.  It was manufactured many decades ago by Moore & Wright in Sheffield, England.  It measures in inches, but has an interesting table engraved on the frame:

micrometer
micrometer

It is too difficult to engrave the cylinder in any other way than in decimal.  The scale there is divided into 25 and four turns will advance by a tenth of an inch.  Notice that they could apparently not resist that factor 4.

I stuck a Lego brick in it.  The scale reads 0.624 inch. The table on the frame (to the right of the brand label) then tells me that is between 0.5937=19/32 and 0.6562=21/32.  It's somewhere halfway between (though one may start to lose patience, staring at those numbers and trying to do interpolation mentally).  I went for 20/32.  That is 15.875mm.  The design length of a Lego brick is 8.00mm×(number of studs) but to eliminate friction with adjacent bricks there is a “gap” of 0.1mm on either side, reducing the actual manufactured length to 8.00mm×(number of studs)−0.2mm in this case 8mm×2−0.2mm=15.80mm; (see the Lego dimensions pages).  The measured length is a little more than expected, perhaps due to temperature or slight deformation on this particular brick.

It's far easier to make this instrument decimal, but then for tradition one converts to fractions in a laborious way, using a table.  Error prone too.

Final Fun

In 2009 I started flying lessons.  What a mess:

Did I get used to it?

Yes.

Because of the “pegs to hang things on” effect.  The quantities are unrelated in their dimensions: altitude in feet does not mix with distance in nautical miles, fuel flow does not mix with anything else at all in daily life.

The distance in nautical miles is perhaps the most difficult:  I know the distances in the area by km.  For example, it's 60km from Geneva to Lausanne, which also has an airport.  But how far is that in nautical miles?

Is it really a Mess?

Most definitely.

I fill the 24 gallon tank from the pump that dispenses in litres

Fuel flow is important to know how long you can still stay in the air;  on the Tecnam P200JF it is 18litres/h and on the Piper Warrior 10gal/h

As mentioned, heading calculations are difficult (multiples of 90 not 100; what is inverse of 345º? should be 145º but is 165º

There is a mysterious “6 minute rule”: because 6 minutes is 1/10th of an hour, and it's easier to calculate in decimal.

Why does this situation persist?  Probably because of sociology:  knowing your way around in the mess makes you a member of the group, it provides a jargon the uninitiated don't understand.

Answer to metric time question

The question was:  what distance do we cover in an hour if we know our speed in metres per second?  The idea was to abandon km/h which is not metric, for m/s which is.  But an hour is not metris either.

So we need to reason completely within a metric system that uses decimalisation also for time.  The second is then 86'400/100'000 of our classic seconds, an hour is 1/10 of a day, or 2.4 of our classic hours. There are 10'000 new seconds in that hour and we are travelling at 1 metre per new second, or 10'000 metres per new hour.  10km/hour.  Pretty slow though, because we would cover only 100km in a day.

Suggestion

You may have noticed that the circle was divided into 400 grades, not 100.  I suspect that was because the grade would have been too big.  At 100 per right angle it was close to the degree of 90 degrees per right angle.

Likewise, dividing the day into 10 hours makes the hours rather too big.  Perhaps we could divide the night into 10 hours and the day as well, then we have 20 hours per day, which is closer to the old 24 hours.

In that case there would be 200'000 seconds in a day, the new second would be about half the old one.  A metre per (new) second would then still be 10km per (new) hour, but we would cover 200km per day.  It would correspond to 8.333km/h in the old hours, or about twice walking speed.  Something we could get used to very well:  walk at half a metre per second, drive in town at 5m/s and on the motorway at 15m/s