How to use math when deciding which perfume to wear

I grew up in a family that loves perfumes. Some of my earliest childhood memories are those of my mom going out with my dad to formal social events in the winter, wearing this unusual, glamorous earthy scent that I had no way of describing as a child but that vividly encapsulated my mom’s personality. Powerful and loving but also enigmatic and defiant.

My grandma, who was always dressed in bright pastel colors, wore sweet, floral, and powdery perfumes. They suited her because she herself was ebullient, theatrical, melodramatic, but also non-confrontational. And, even my dad, who isn’t one to spend time overanalyzing beauty products, allowed my mom to choose a small collection of colognes for him—often spicy, balsamic, and a bit woody—that complemented his warm but strong-willed nature.

My brother and I, as a result, got exposed to this hobby early on and learned to appreciate the art of perfume-wearing. I wasn’t aware this contextual education was happening, but as I got older and as my collection grew, my friends would point out that it was unusual I had so many perfumes, and that I had strong opinions on when and which perfume to wear. To me, of course, it wasn’t unusual because this had always been a thing in my family.

Interestingly, I only realized later that my way of deciding when to wear which perfume was very different from that of my family. While my mom, for example, can instantaneously break down each perfume into top, middle, and base notes, which somehow tell her when to wear it, my mind thinks very mathematically. When I first try on a perfume, I see an image in my head, one that I can clearly contextualize with the help of time, temperature, and weather. And then, my mind translates those features to math.

That math is something that I regularly use to choose which perfume to wear, and something that I think can bring a lot of ease to everyone’s decision-making.

The 3D Cartesian coordinate system for perfumes

For me, each perfume can be a placed in a three-dimensional Cartesian coordinate system, where the x axis represents the time of day, the y axis represents external temperature, and the z axis represents precipitation.

On the x axis, we move from day to night. On the y axis, we move from hot to cold. And, on the z axis, we move from clear to rainfall. I make the z axis simplified on this chart because I usually consider any form of precipitation, rain or snow, at the “rainfall” end of the spectrum.

Now, when we talk about Cartesian coordinate systems, we have to have some form of numbers represented on these axes to describe position.

For simplicity, I like to imagine that each axis is bounded by —1 and 1 as the terminal points. What that means is that on the x axis, just as an example, —1 would represent the late night and 1 would represent the early morning, just after sunrise. On the y axis, on the other hand, we can imagine that —1 would mean really cold weather and 1 would mean really hot weather.

Keep in mind that these terminal points on each axis are directional at best; they are not mapped to the exact magnitude of these situations in real-life scenario. In other words, when I say 1 on the y axis, I don’t think of it as boiling-level temperature, but instead as just the regular summer heatwave.

You can start to place various points in this space and identify what they would mean in real-life scenario. For instance, what would the origin O with x = 0, y = 0, z = 0 mean?

For the x axis, that would refer to twilight, that majestic moment between the day and the night. Though, in the context of perfume-wearing, I am really referring to the time just after sunset, because I could not imagine myself waking up and timing perfumes before sunrise.

For the y axis, that would refer to the perfectly moderate, mild temperature of the environment that’s neither hot nor cold, which for my body is 21°C or 70°F.

Finally, for the z axis, that would mean the classically cloudy day, when you are not able to see the sun at all but there is also no rain or snow.

Together, that would imply that the origin O would represent a moderate 21°C or 70°F cloudy day, just after sunset. Who thought that dreadful high school math would turn out to be actually applicable?

My favorite perfumes in the 3D Cartesian coordinate system

Let’s see how some of my favorite perfumes can be described in a 3D Cartesian coordinate system. I picked out the three that I think are very different in their olfactory composition and intended use: Fahrenheit by Dior, Un Jardin sur le Nil by Hermès, and Yatagan by Caron.

Fahrenheit was a cologne that I discovered in 2018 and instantly fell in love with. The moment I smelled it, I knew it was a statement scent. Spicy, citrusy, woody, and leathery, with a prominent underlying note of gasoline, I instantaneously saw myself wearing it when going out at night, wearing a punk-inspired jacket, black leather boots, a sweater or a shirt with skull imagery.

So, my mind translated that imagery to: late night, crisp cold but not freezing weather, and clear skies—because I don’t do rainy nightlife. Mathematically, I therefore assign Fahrenheit to point D_F in space with coordinates x = —1, y = —0.5, and z = 1.

Un Jardin sur le Nil was one that I was introduced to by my mom. I distinctly remember seeing her wear it in springtime, often when she had to attend a work lunch, when she would also sport a sophisticated, chic outfit. At the same time, the perfume with its floral and citrusy notes, mango being the most prominent one, gave her a playful edge.

As a result, my mind always associated this one with an image of a gentle but playful butterfly, flying on a bright day, in peak spring, when it’s usually clear with maybe an occasional spring rain that gives even more life to all the beautiful nature around us. Mathematically, I therefore assign Un Jardin sur le Nil to point H_N in space with coordinates x = 1, y = 0.35, and z = 0.75.

Yatagan I discovered while reading an interview with the incredible Iris Apfel. She mentioned that she and her husband Karl used the same perfume by Caron, which was not very popular at the time. After some research online, and perusing many people’s reviews, I found it for a very reasonable price and decided to do a blind buy. I have always been such a fan of Iris, I figured she must know if something is good.

I remember opening the box when it came and seeing this amber, chic-looking perfume bottle with dark-red letters spelling out Yatagan (later on, I learned it was a type of Ottoman knife) in a font that very much reminded me of the Prince of Persia video games.

The first whiff gave me strong wood and forest imagery. I liked it. I imagined myself walking through a dense forest on a fall day, stepping on freshly fallen autumn leaves, damp from all the rain, which accentuated the smell of the surrounding pine trees. Mathematically, I therefore assign Yatagan to point C_Y in space with coordinates x = 0.25, y =— 0.5, and z = —0.8.

Each perfume that I discovered or was introduced to was therefore always followed by an initial imagery, which I could always describe using the time of day, external temperature, and precipitation. My mind would then map the components of this imagery to a three-dimensional Cartesian coordinate system.

And that’s how I ended up with a list of all my favorite perfumes with their x, y, and z coordinates. Whenever I have to decide which perfume to wear, I observe what the day is like and consult my little database of coordinates.

Using the 3D coordinate system to group perfumes by their vibe

What’s cool and fun about placing perfumes in a 3D coordinate system is that we can calculate the distance between two perfumes. This distance is what my mind sees as the difference in their “vibe”.

Because this 3D coordinate system has contextual significance, with each axis representing something that we experience with our senses, the proximity of perfumes in this space tells us that they elicit a similar… well, for lack of better word, vibe.

That distance can be calculated using the well-known equation for calculating the distance between two points in a three-dimensional Cartesian coordinate system. The larger the distance, the greater the difference in vibe.

For orientation, it’s useful to identify the smallest possible distance d_min and the greatest possible distance d_max between two points. The smallest distance is obviously zero. The greatest distance is less obvious, so we actually need to calculate it. The formula above shows that the greatest distance will happen for points P₁ (1, 1, 1) and P₂ (—1, —1, —1), whose distance in vibe is 3.46.

In my personal collection, as seen in the tables above, Terre d’Hermès Eau Tres Fraiche has coordinates x = 1, y = 1, z = 1. I don’t, however, have any perfumes that have x = —1, y = —1, and z = —1. The closest perfume to that theoretical point P₂ is Promise by Frederic Malle, with coordinates x = —1, y = —1, and z = —0.4.

These two perfumes are indeed almost the complete opposites. Their vibes are very different.

Terre d’Hermès Eau Tres Fraiche is a pleasant, zesty, inoffensive summer fragrance that’s perfectly suited for a day on a boat, wearing a light, breezy white shirt, white chinos, and beige espadrilles.

Promise is a bold, risky, and very divisive scent that I can pull off only when I am feeling incredibly confident and even a bit cheeky. It’s sexy, intoxicating, and frustrating. It juxtaposes rosy, woody, and spicy notes, which means it rebels. And rebelling means it’s not a crowd-pleaser, so I wear it only when I feel really good about myself.

It can be hard to visualize how vibe relates to mathematical distance, so let’s plot two perfumes, Fahrenheit and Un Jardin sur le Nil, that we placed previously in the 3D space and calculate the distance between them.

Looking at the chart, we can see that these two perfumes also have a decent distance between them, which means we should expect that the math would tell us the difference in their vibe is high—not 3.46 maybe, the greatest possible distance, but at least somewhat high.

2.19 is a solid distance! And that number correctly shows how I—and, I imagine, many other owners of both perfumes—feel about their opposing vibes. Fahrenheit is a gritty nightlife perfume, while Un Jardin sur le Nil is a sophisticated, garden party perfume. They are, however, brought closer together in space by being best suited for days with clear skies, which is why their distance in vibe is not as high as 3.46.

Final thoughts

Nailing down the art of knowing when and which perfume to wear is a fun and rewarding undertaking. I always enjoy learning how others choose their perfumes and how their minds analyze them.

If you are someone who is not into perfumes, but would like to know more, I recommend starting with Fragrantica. It’s like an encyclopedia of all perfumes out there, and a wonderful place to learn the major names in perfumery, to understand how others choose perfumes for their collections, and to pick up all the cool incisive vocabulary that will help you describe olfactory experiences in a far more nuanced way.