Guesses have a strange way of disguising themselves as facts, and taking root in popular knowledge. Consider the claim that the human nose can distinguish between 10,000 different smells. The statement crops up in all manner of websites, along with textbooks and scientific publications.

The figure came from a paper published in 1927, which suggested that people could tell the difference between odours according to four different qualities—fragrant, acidic, caprylic, and burnt—along a nine-point scale. That gives us 6,561 distinguishable smells, which was later rounded up to 10,000!

And that’s it.

There wasn’t any evidence for any of these assumptions, but that didn’t stop an uneducated guess from becoming enshrined as fact.

When Andreas Keller at Rockefeller University learned about this, he was dissatisfied. He wanted to come up with a better estimate—one rooted in actual experiments.

Similar estimates already exist for vision. We know that our eyes are sensitive to wavelengths of light between 390 and 700 nanometres—that is, from red to violet. By doing comparisons within that range, scientists have shown that we can tell the difference between 2.3 million and 7.5 million colours.

The same applies to sound. We can hear frequencies between 20 and 20,000 Hertz—from four octaves below middle C to many octaves above it. Within that range, we can discriminate between around 340,000 tones.

But colours and tones are easy to probe. Both vary along a single dimension: wavelengths of light and frequencies of sound, respectively. Smells don’t have an equivalent. They are complicated cocktails of molecules; a rose, for example, owes its scent to some 275 ingredients. There’s no single metric that we can measure these against; instead, we’re forced to describe them with subjective adjectives. And unlike light and sound, which we can perceive within certain boundaries, there is potentially no limit to the combinations of molecules that could make up an odour.

To estimate the bounds of our sense of smell, Keller had to get creative.

He gave volunteers three jars, two of which contained the same smell. Their job was to find the odd one out. The team made the smells from the same pool of 128 ingredients, which were mixed together in groups of 10, 20 or 30. They then paired these mixtures up so that some pairs had no ingredients in common, some were almost identical, and most were somewhere in between. Each volunteer sat through 260 of these discrimination tests.

After crunching the numbers, the team found that when the pairs of mixtures overlapped by less than 51 percent, most of the volunteers could tell the difference between them. And if they overlapped by less than 57 percent, most of them were distinguishable. This means that the average person can tell the difference between 1.7 trillion (that’s 1,700,000,000,000)different combinations of 30 ingredients.

“It’s one of those moments you live for as a scientist: reframing a problem and finding the solution out in left field,” says Avery Gilbert, a smell scientist who first tracked down the origins of the spurious 10,000 number.

The 1.7 trillion figure is an average. At least one person in the study had an exquisitely sensitive nose that could potentially discriminate between more than 10 million trillion trillion combinations of 30 ingredients. Another volunteer could only make out around 70 million of them.

There’s good reason for this variability. The genes that create smell receptors—the proteins that recognise the molecules we inhale—are the largest family of genes in our genome. They’re also more variable than other genes. “As a consequence, everybody smells the olfactory environment with a different set of receptors and therefore perceives it differently,” says Keller.

The 1.7 trillion figure is also a gross underestimate. “There are probably billions of odorous molecules and we only worked with 128 of them,” says Keller. “Furthermore, we only mixed 30 components. There are many more mixtures with 40 or 50 components.”

Still, a trillion smells is still many more than the number of colours or tones we can perceive. There’s good reason for that too. “Smell evolved to help us detect small differences between different smells: the smell of my baby compared to the smell of my neighbour’s baby, or the smell of fresh milk compared to the smell of spoiled milk,” says Keller. “There really is no need to discriminate trillions of smells, but there is a need to discriminate very similar smells. As a consequence, we can discriminate very many different smells.”

“The numbers are staggering yet not that surprising,” says Gilbert. “Smell is, above all, a combinatoric sense. There is a large but finite number of odorous molecules in the world and they occur in an endless array of mixtures and concentrations. Yet here we are, sniffing at them and making these incredibly fine discriminations on a daily basis. We handle the complexity pretty well.”

“If we couldn’t discriminate a trillion different mixtures where would we be?” he adds. “We’d know when to take the garbage out, but we wouldn’t be able to tell one vintage of Bordeaux from another. In fact, if we couldn’t discriminate millions of combinations we wouldn’t have bothered to create Bordeaux in the first place.”