"One-way functions" By Luca Turin

"One-way functions" By Luca Turin

I have never gone to perfume school, and it is sadly too late for me to do so, but I can imagine how the student perfumer feels when first given access to the full palette of raw materials. When I was nine years old, I used to sit at a Bechstein concert grand that belonged to family friends and, as the British say, “tickle the ivories”. Even simple chords were so beautiful, especially with the sustain pedal held down, that it was easy to understand why sung polyphony was the greatest hit for centuries. But the strange thing was how different the component notes of a chord were from the chord itself, how mysterious the added magic of playing them together. A chord never felt like the sum of its parts, some other operation seemed to be at work.

We now know that the perception of harmonies involves the comparison and matching of all the frequencies contained in each of the notes, such that the analysis our brain performs so willingly is more akin to the product of several Fourier transforms, one for each note. Such operations are not easily invertible: to dissect a complex chord into its component notes requires practice, and can be near-impossible when tricks are played with timbre: when Egberto Gismonti and Mauro Senise play a fast tune called Lôro on piano and flute in exact unison it sounds for all the world like a new instrument, a concert grand made of Baccarat crystal. Listen to 30 seconds of it on iTunes, and I am sure you’ll agree that no computer would give the correct answer.

Perfumery chords are no different: the classic bergamot-cistus-oakmoss of chypre is, once invented, as self-evident and capacious as perspective drawing. It’s as if the citrus-sweet-bitter were orthogonal axes of an invisible space, and once you had made them appear into thin air you could then put in walls and floors, hang paintings, slide sofas, move in and have a party. Even binary accords can have non-invertible magic. The vetiver-vanilla accord, once explained, falls to the floor with a loud crash and is very hard to put together.

If someone you know loves Habanita, don’t tell them how it’s done. Of course these days professionals use gas chromatography and mass spectrometry to analyze the competition and replicate it. It is easy with synthetics and harder but still doable with naturals. But how did they copy fragrances in the old days? An old perfumer told me that you could do it by identifying one raw material, smelling it pure to desensitize your nose, smelling the original mix again from which that one would now be “missing”, identifying another etc.

Such was the power of this chemical cryptography, however, that until recently, merely splitting the formula in half and never giving a single person access to all of it would guarantee its unbreakability. This is the exact equivalent of public-key cryptography: Guerlain publishes the product of two large primes, and only Jean-Paul knows both numbers. The rest of us smell a 128-digit marvel.