4.6 — Measures, Units and Where They Came From

Every unit was once a physical object or a body part, and the two-century project to replace all of them with something nobody can lose finished in 2019.

The metric system

Where did the metre come from?

From an attempt to define a unit that belonged to nobody.

The French Revolution wanted units not derived from a king's arm, and the natural candidate was the Earth itself. In 1791 the metre was defined as one ten-millionth of the distance from the North Pole to the equator, along the meridian through Paris.

Two astronomers, Delambre and Méchain, then spent seven years surveying the arc from Dunkirk to Barcelona by triangulation, through a revolution, being arrested repeatedly as suspicious persons carrying strange instruments. Méchain found a discrepancy in his measurements at Barcelona, could not reconcile it, concealed it, and reportedly went to his grave tormented by it — he died of malaria in 1804 while trying to extend the survey and correct it.

The result was slightly wrong, by about 0.2 millimetres, mostly because the Earth's flattening was not known accurately. It did not matter: a physical bar was made from the survey and became the standard in its own right. That platinum-iridium bar in Sèvres near Paris defined the metre until 1960.

It is now defined from the speed of light: the distance light travels in vacuum in 1/299,792,458 of a second. That number is peculiar because it was chosen to keep the new metre identical to the old one.

Why was the kilogram a lump of metal until 2019?

Because mass was the last quantity for which nobody could find a better definition.

Length went to light in 1960 and the second went to atomic transitions in 1967. Mass stayed as a physical object: a platinum-iridium cylinder about the size of a plum, kept under three nested glass bell jars in a vault in France since 1889. Forty official copies were distributed to countries, and every kilogram in the world was traceable to that one object.

The problem was discovered by comparing it to its copies every few decades. They drifted apart — by around 50 micrograms over a century. Nobody knew whether the original was losing mass or the copies were gaining it, and there was no way to find out, because the definition was the original. By definition it weighed exactly one kilogram even as it changed.

In 2019 the kilogram was redefined in terms of the Planck constant, fixed at an exact value, connected to mass through quantum mechanics and realised in practice with an instrument called a Kibble balance that measures mass against electrical quantities. The entire International System is now defined by seven fixed constants of nature, and any sufficiently equipped laboratory anywhere — or on another planet — can reproduce every unit from scratch.

The old cylinder still exists. It is now an object of historical interest whose mass is measured rather than assumed.

Why does the United States not use the metric system?

It legally does, and has since 1866 — the metric system is the official basis of American measurement, and the customary units are defined in terms of it. An inch is exactly 25.4 millimetres by law.

What did not happen is adoption in daily life. The Metric Conversion Act of 1975 made conversion national policy and made it voluntary, and voluntary conversion largely did not occur. Road signs, groceries, weather and construction stayed customary.

There is a documented cost. The Mars Climate Orbiter was lost in 1999 because one team supplied thrust data in pound-force seconds and the receiving software expected newton-seconds; the spacecraft entered the atmosphere too low and broke up. The mission cost around $125 million.

American science, medicine and the military run entirely metric, and American manufacturing largely does. The result is a country where an engineer works in millimetres and buys milk in gallons.

Temperature

Why are there three temperature scales?

Because two were built around convenient reference points and the third around physics.

Fahrenheit (1724) set zero at the coldest temperature Daniel Fahrenheit could reliably reproduce — a mixture of ice, water and ammonium chloride — and set 96 at roughly human body temperature, a number chosen because it divides neatly by 2 repeatedly. The scale was later adjusted to fix the freezing and boiling points of water at 32 and 212, which is why body temperature ended up at the untidy 98.6.

Celsius (1742) used water: zero at freezing, 100 at boiling, at standard pressure. Anders Celsius originally had it the other way up, with zero at boiling, and it was inverted after his death.

Kelvin (1848) starts at absolute zero, the point at which a substance has the least possible thermal energy — there is nothing below it, because you cannot have less motion than none. Its degrees are the same size as Celsius, so 0 K is −273.15 °C.

Kelvin is the one that behaves properly in equations. Doubling the Kelvin temperature of a gas genuinely doubles the average kinetic energy of its molecules; doubling the Celsius temperature means nothing at all, because the zero point is arbitrary. That is why every physical law involving temperature uses kelvins.

Absolute zero has never been reached and cannot be, though laboratories have got within a few billionths of a degree.

Logarithmic scales

What is a decibel, and why is it confusing?

It is a ratio expressed logarithmically, not an amount — which is why "decibels" alone means nothing until you say decibels of what, relative to what.

Sound pressure in air is quoted as dB SPL, relative to a reference roughly at the threshold of human hearing. The logarithm is used because the range of audible sound is enormous: the loudest tolerable sound has a pressure around a million times the quietest audible one, and a linear scale would be unusable.

The consequences trip people up constantly. An increase of 10 dB is ten times the sound power and is perceived as roughly twice as loud. An increase of 3 dB is double the power and barely perceptible. And decibels do not add: two identical machines at 80 dB each produce 83 dB together, not 160.

Useful anchors: a quiet room is around 30 dB, normal conversation 60, a busy road 80, a rock concert 110, and a jet engine at close range 140, where damage is immediate. Sustained exposure above about 85 dB damages hearing permanently, and the damage is cumulative and irreversible.

The unit is named after Alexander Graham Bell. The bel was too large to be convenient, so the decibel — a tenth of one — is what is actually used.

What does pH measure?

The concentration of hydrogen ions in a solution, on a negative logarithmic scale.

Each whole step is a factor of ten. A solution at pH 3 has ten times the hydrogen ion concentration of pH 4 and a hundred times that of pH 5. Pure water at 25 °C is pH 7, acids are below, alkalis above.

That logarithm makes the everyday numbers more dramatic than they look. Stomach acid at around pH 1.5 to 3.5 is roughly a hundred thousand times more acidic than water. Lemon juice is around pH 2, vinegar 2.5 to 3, black coffee 5, blood is tightly held between 7.35 and 7.45 — and a drift outside that narrow band is a medical emergency, which is a good illustration of how much work the body does to keep it there.

Ocean acidification is a case where the small numbers matter. Ocean pH has fallen by about 0.1 since the industrial revolution, which sounds trivial and is a roughly 30 per cent increase in hydrogen ion concentration.

Older units that survive

Why is a horsepower a horse?

Because James Watt needed to sell steam engines to people who currently owned horses.

He measured the work a mill horse could do turning a wheel, and defined a unit around it so a customer could ask how many horses an engine would replace. He set it at 33,000 foot-pounds per minute — around 746 watts.

It is a generous figure. A real horse can exceed it briefly but cannot sustain it all day; Watt was not underselling. A fit human sustains roughly 0.1 horsepower over an hour and can peak above one for a few seconds.

The metric horsepower used in continental Europe is slightly different, at 735.5 watts, which is why the same car is quoted at different figures in different markets.

What is a knot, and why do ships use it?

One nautical mile per hour, and the nautical mile is the useful part: it is one minute of arc of latitude, about 1,852 metres.

That definition makes navigation arithmetic trivial. Sixty nautical miles north is exactly one degree of latitude. On a chart, distance can be read straight off the latitude scale at the side, with no conversion.

The name comes from the measuring method. A log on a line was thrown over the stern, and the line had knots tied in it at fixed intervals. A sailor counted knots running out through his hands in a fixed time measured by a sandglass. The number of knots was literally the speed, and the word for the instrument gave us the ship's logbook.

Why is a carat a carat?

Two different units share the name, which is the source of endless confusion.

For gemstones, a carat is a mass: exactly 200 milligrams. The word comes from the carob seed, which was used as a counterweight in ancient markets because the seeds were believed to be unusually uniform in mass. They are not especially uniform, as it happens, but the tradition held until the unit was standardised in 1907.

For gold, a karat is a purity: parts of gold in 24. So 24K is pure, 22K is 22 parts gold and 2 parts other metal — 91.6 per cent, which is the number stamped on Indian jewellery — and 18K is 75 per cent. Twenty-four exists as the denominator for the same reason twelve runs the clock: it divides cleanly by 2, 3, 4, 6, 8 and 12.

What is a calorie, and why are there two?

A calorie is the energy needed to raise one gram of water by one degree Celsius. That is a very small amount, so food energy is quoted in kilocalories — a thousand of them.

The confusion is that food labelling calls a kilocalorie a "Calorie", sometimes with a capital C and often without any distinction at all. A 200-calorie biscuit contains 200,000 calories in the scientific sense. Most countries now print kilojoules alongside, which avoids the problem entirely: one kilocalorie is about 4.18 kilojoules.

Food energy is measured by burning the food in a sealed chamber and measuring the heat, then adjusting for what the body cannot absorb. That is why the numbers are approximate in a way people underestimate — the labelled figure does not account for how much of it your particular digestion extracts, which varies with the food's structure and how it was cooked.

Digital units

Why does a 1 TB hard disk show up as 931 GB?

Because two different systems both use the prefix and disagree by a growing margin.

The metric prefixes mean powers of ten: kilo is 1,000, mega is 1,000,000, giga 10⁹, tera 10¹². Computers, however, address memory in powers of two, and 2¹⁰ = 1,024 is conveniently close to 1,000. So early computing borrowed the metric prefixes for the binary quantities, and a "kilobyte" came to mean 1,024 bytes in some contexts and 1,000 in others.

The gap grows with each step. At kilo it is 2.4 per cent. At mega, 4.9. At giga, 7.4. At tera, 10 per cent.

Disk manufacturers use the decimal meaning, because that is what the prefixes mean. Windows reports using the binary meaning while printing the decimal label. So a disk holding 1,000,000,000,000 bytes — an honest terabyte — is displayed as 931 "GB", where the operating system means 931 × 1,024³.

The standards body settled this in 1998 and almost nobody adopted it. The binary units have their own names and symbols: kibibyte (KiB) = 1,024 bytes, mebibyte (MiB), gibibyte (GiB), tebibyte (TiB). Linux and macOS have largely moved to reporting decimal units correctly; Windows has not.

What comes after terabyte?

The full sequence, each a thousand times the last:

Unit	Decimal size	Roughly
kilobyte KB	10³	a short email
megabyte MB	10⁶	a photograph
gigabyte GB	10⁹	a film
terabyte TB	10¹²	a laptop disk
petabyte PB	10¹⁵	a large company's archive
exabyte EB	10¹⁸	global internet traffic in a few hours
zettabyte ZB	10²¹	annual global data creation
yottabyte YB	10²⁴	not yet meaningful

Two more were added in 2022 — ronnabyte at 10²⁷ and quettabyte at 10³⁰ — largely because the sequence was running out of headroom for scientific data.

A bit and a byte are not the same and the difference matters commercially. A bit is one binary digit; a byte is eight of them. Storage is quoted in bytes and network speed in bits per second, so a "100 Mbps" connection downloads at about 12.5 megabytes per second at best. The abbreviation carries the distinction: capital B is bytes, lowercase b is bits.

Why is a byte eight bits?

It was not always. Early machines used bytes of six, seven and nine bits, and the word originally meant "however many bits are needed for one character".

Eight won because IBM's System/360 in 1964 standardised on it, and the System/360 was successful enough to set the industry's conventions. Eight bits gives 256 values, which is enough for the Latin alphabet in both cases, digits, punctuation and control codes with room to spare — and it is a power of two, which makes address arithmetic clean.

The word nibble for four bits, half a byte, is a real term and not a joke, though it began as one. It matters because one nibble is exactly one hexadecimal digit, which is why memory addresses and colour codes are written in hex.

What comes next

The next Part turns from measuring to mapping — countries and borders and flags, the superlatives, and why a world map lies about the size of Africa on purpose.