The spaces of aromas

There is nothing mysterious in the sense of smell. The modern representative of the genus Homo is a happy owner of about 350 working varieties of olfactory receptors. Each smelling substance can interact with one or more receptor. Each receptor is able to interact with many substances. Each smell is a mixture of substances. Theoretically, in the presence of the necessary initial data, any smell can be represented in the form of a calculated point in the 350-dimensional space of aromas.

This is a standard, working, established approach. Everyone is familiar with the three -dimensional spaces of the RGB or CMYK color, the dimension is strictly equal to the number of varieties of cones on the retina. Taste is also a space, but already five -dimensional, by combining five basic tastes you can recreate any necessary.

With smell, everything is exactly the same. Only measurements are more. And a system consisting of 350 receptors is very difficult to formalize. There is no doubt that one day they will do it. But today it is too complicated and, in general, far from a priority task. Today you have to use approximations.

The most ordinary sensory analysis is such an approximation. It is based on the allocation among the characteristics of the fragrance of the most important and affixing to these characteristics-concripators of assessments. We can say that we are talking about reducing the dimension of the space of aromas to the degree of "convenience of work".

How does this work? Let, you need to assess the aroma of vanilla. To do this, do not evaluate all possible shades of smell. We distinguish important descriptors: vanilla, sweet, wood, fruit, phenol, smoky. Specialists affix assessments of the severity of descriptors. The averaged result will be a point in the space of the sense of smell, but the dimension is much less than 350, usually not more than 10. strictly in terms of the number of desecrips used. After analyzing several similar aromas, we can clearly see the difference between them. Not in abstract and incomprehensible expressions “brighter”, “vanilla”, but a quantitative difference. If we need to analyze another smell, such as apples, we choose another set of descriptors. This is fine. Well, you won’t look for citrus notes in vanilla, and vinegar in oranges?

In fresh work on the subject ( http://dx.doi.org/10.1371/journal.pone.0073289 ) a group of mathematicians proposed its, mathematical, and even more simplified vision of the sense of smell. The authors analyzed the guide of 144 aromas, gaining a total of 146 descriptors. Combined close smells. We watched their distribution throughout the space of smells. Built a model. They concluded that all known smells are derivatives of ten basic aromas: perfumery, wood, fruit, chemical, mint, sweet, popcorn, lemon, caustic and putrefactive. Ten dimensions, in their opinion, are enough to model all smells. Funny. I wonder why they should not try to describe the smell of beef in their model and explain how it will differ from the smell of milk?

At the same time, the authors of the ten -dimensional model claim that their finding will help the work of perfumers and expand the understanding of the mechanism of perception of odors. It's funny again. I see nothing that she can expand. I don’t know where, how and to whom it can help, except that the authors themselves in writing the next work. No, I have no complaints about theory and mathematics. But I have claims to practice.

The first claim is semantic. Alas, it is technically impossible on the basis of a verbal description from the reference book to mathematically accurately reproduce the smell. Based on sensory analysis with the participation of professional tasters, it is possible. And on the basis of a verbal description, it is impossible. There is not enough wealth. Here, guess what the smell is: sweet, tart, fruit, floral? Apricot? They didn’t guess, this is a lilac. And mathematicians would have decided that it makes no difference.

The second claim is semantic. This does not happen. I explain. Suppose we have a detail, and we need to get its plausible image on the plane. This can be done for a specific detail by projecting its image on a convenient plane. But we cannot come up with such a single universal plane, the projection on which would conveniently reflect all existing details on the planet. So with smells. A sensory analysis is a projection of the “all smell” on the “subspace” of the sense of smell convenient for work. But, alas, there is no such universal “subspace” in the size of 10, which would see all smells at once. There is even approximately exists.

And in general, why 10, not 5? Why not 13 or 666? Ah, so it happened and you can't say against the results? And why then did not work 32, as in another, similar work ( www.sciencedirect.com/science/article/pii/s0925231202008056 )? True, there was a much more detailed reference book in it: 851 aroma and 278 descriptors, and it is mentioned that the error of the 32-dimensional model is several percent. This is a very big mistake from a practical point of view. She, of course, is less than the differences between beer and ketchup. But in a few percent, an important difference between chicken and fish, orange and lemon, pear and apple will easily fall. Moreover, the difference between Antonovka and the barn, perfectly captured by sensory analysis, will go unnoticed. Ten selected "local" measurements are usually enough to model a specific smell during sensory analysis. But even 32 “general” measurements are notly enough to simulate signals from 350 receptors at once. Eh, you.

Dear mathematicians! You are smart and good people. In general, you are right. In the sense of smell, of course, there is nothing mysterious.

But not the same?