Our world is ordered with rigid measurements - but alongside them are much more human ways to scale such things as the ferocity of storms and the strength of chilis.

How much spicier is a Scotch Bonnet chili pepper than a Bird’s Eye? How much harder is diamond than quartz? If a jiffy is quick, is a shake even quicker, and a Warhol the quickest of all?

Scales help us measure the physical world. To compare quantities, we mostly rely on quantitative scales – numerical measurements that tell us something about frequency and quantity. Inches, feet, yards and miles; ounces, quarts, litres and gallons; seconds, minutes, and centuries are all quantitative scales. But what about qualitative scales?

These are yardsticks that measure observable, but not necessarily numerical, properties – and we use them all the time. Qualitative scales are sometimes humorous and often downright bizarre, but they are just as valuable as quantitative scales for imagining relationships between properties and standardising ideas.

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They range from chili pepper heat to mineral hardness to ocean breezes to something called the Mother Cow Index (formerly used in real estate transactions in the American Southwest, the MCI was the number of pregnant cows an acre of a given plot of land could support). Qualitative scales allow us to label variables with little or no quantitative information. These unusual units of measurement are often colloquial: guesstimations and “as-the-crow-flies” rules of thumb that allow for quick assessments and comparisons.

Yet qualitative scales prove their usefulness time and again. Without them, we would struggle to conceptualise ideas of pain (a doctor might ask a patient to rank his symptoms) or grade the severity of weather conditions (like the Beaufort Scale does).

Date, when measured from an arbitrary epoch such as BC or AD, helps us understand time, while direction measured in degrees from true or magnetic north orients us in physical space.

Quantitative scales are much easier to evaluate, since they are effectively comparisons to a known standard. A square-kilometre, a teaspoon of sugar or an hour-long lecture are basically unchanging measurements. Qualitative scales are more subjective. Neither quantitative nor qualitative scales, however, are ever 100% accurate: they are each limited by the uncertainty baked into the definitions of units themselves.

Beaufort may have developed the first modern qualitative scale

Any true measurement, when you get down to it, is arbitrary. Yet the very human urge to appraise, quantify, and compare persists, and so we continuously seek new ways to describe our experience of the world.

In 1805, Rear Admiral Sir Francis Beaufort, an Irish hydrographer in the Royal Navy, wanted a way to more accurately measure ocean breezes. Each day aboard the HMS Woolwich, he recorded in his diary wind force and sea conditions, from eerie calm to violent gales. Today, a “Beaufort 0” means an ocean as smooth as glass, while a "Beaufort 12" indicates crashing waves, hurricane-force wind, whitecaps and greatly reduced visibility.

In between these extremities are gentle breezes and fresh breezes and moderate breezes (yes, these are all different breeze strengths). Beaufort may have developed the first modern qualitative scale: a ranking in which the order of values is significant, but the difference between each value is not really known.

By and large, qualitative scales fall into one of two categories: Ordinal measurements (in which values can be arranged in a meaningful order), or Interval measurements (in which values can be arranged in a meaningful order, and the difference between two values matters). For example, an earthquake that measures 6.0 on the Richter scale is many orders of magnitude greater than a small trembler of 3.0. So the order of quake size matters, and the interval is also fixed, meaning that Richter’s scale is an Interval scale.

Grades such as beginner, intermediate and advanced, by contrast, are Ordinal. Who can say what the exact difference is between a novice and an expert, or where one classification ends and the other begins? Another way to put it: Ordinal scales allow for the difference among items, but not the ratio between them.

An “extremely satisfied” response on a customer service ranking is not triple the satisfaction of “somewhat dissatisfied”; even the difference between 10C and 20C, while quantitative, is not an intuitive measurement. Some argue that these limitations make qualitative scales inherently less functional.

There are things that we can measure and things we can’t – Andrew Hanson

Indeed, while proper measurement ascribes value to the physical world, our perception of the physical world varies widely. “There are things that we can measure and things we can’t,” says Andrew Hanson, senior research scientist at the National Physical Laboratory (NPL) in the UK. “But even what we can measure, we can only do to a degree.”

Hanson works in soft metrology: he studies measurements that relate to sensory scales like colour and light, which are quantitative but also subjective. No human can see ultraviolet or infrared light, but even shades on the visible spectrum appear differently from person to person – a difference that has real-world implications.

Think about traffic signals, which must appear red, amber, or green. The way we perceive the brightness of these coloured lights is non-linear: numerical changes in input (watts) don’t always translate to the naked eye, or to human experience.

“For a scale to become legitimate, everyone must agree on its units and intervals,” Hanson explains. Despite the fact that they aren’t always linear or mathematical, qualitative scales still seem to get the international greenlight.

Take the Scoville scale. Named after its creator, American pharmacist Wilber Scoville, this scale ranks chili pepper spiciness. But the Scoville doesn’t actually measure the amount of spice, or capsaicin, in a pepper; rather, it notes the number of dilutions needed to put out a capsaicin-fueled fire.

A habanero pepper, for example, must be diluted 3,500 to 8,000 times, while a garden variety bell pepper needn’t be diluted at all. Because no two tongues experience capsaicin the same way, the American Spice Trade Association came up with measuring pepper heat in Scoville Heat Units (SHU), a method standardized in 1998. The spiciest pepper in the world is tied between the Carolina Reaper and the Dragon’s breath, which tops out at a blistering three-million SHU.

Lord Kelvin, who had a unit named after him, reasoned “when we cannot measure a thing in numbers, our knowledge is of a meagre and unsatisfactory kind”

After all that heat, a cold drink might be in order. Metrologists beware: your glass of whiskey may not be the same size from one pub to the next, or even the same strength. The shot is a liquid volume measure that varies from country to country and state to state depending on legislation, while a spirit’s proof has only recently been standardised (until the 20th Century, alcoholic spirits were assessed by mixing them with gunpowder and testing the mixture to “prove” that it would ignite).

The shot is routinely used for measuring strong liquor or spirits when the amount served and consumed is smaller than the more common measures of alcoholic “drink” and “pint” – each themselves qualitative measures.

Lord Kelvin, who had a unit named after him, reasoned “when we cannot measure a thing in numbers, our knowledge is of a meagre and unsatisfactory kind”. But sometimes numbers don’t quite hit the spot, and that’s where qualitative scales come in.

These scales are what allow us to express the size of a sinkhole as a Double Decker Bus (DDB). They give us a Royal Albert Hall’s worth of rubbish in a landfill (the volume of the famous London auditorium is between 3 and 3.5 million cubic feet). They even help us to measure beauty. One Helen is enough to launch one thousand ships (a milli-Helen launches but one), while a sapphire’s absolute Mohs is a perfect 10 (the Mohs Scale of Hardness measures a mineral’s resistance to being scratched). Measurement – whether qualitative or quantitative – underpins virtually all aspects of human activity.

“Measurement is the comparison of something unknown against something known,” says Hanson. Better measurement enables better science, less waste, and greater precision in fields like engineering and healthcare, which in turn means a better quality of life. Someday, we might be able to put numbers to ideas like pain or happiness, turning qualitative measurements into true quantitative scales.

At present, qualitative measurements help us translate ideas that are almost poetically incalculable: the length of a city block or the Grand Canyon, the pitch of a teakettle or a lightning strike or a whisper in the dark.

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