In last week’s post about taste and smell I cited a study that estimated that humans can smell over a trillion different odors. That study was published in *Science *earlier this year by Leslie Vosshall’s lab at Rockefeller University.^{1} While the paper was a bit controversial from the start, this week I discovered that the controversy has reached a new level due to a scathing rebuttal just published online by Markus Meister, a professor at Caltech.^{2} I’m going to devote today’s post to discussing this controversy because I think it reveals a lot about how we scientists make assumptions, pick fights, and often struggle the hardest to answer the simplest questions.

### It’s a smelly world out there

The basic question is quite simple: how many different smells can we perceive?

Smell occurs when your nose detects chemicals wafting through the air. Most of the smells we perceive are composed of many chemicals mixed together. The scent of a rose, for example, is produced by a mixture of 275 different molecules.^{3} There are millions of different chemicals in the world that can be combined in an almost infinite number of combinations. But not all of those mixtures smell different, and some don’t have any odor at all. What we want to know is, how many different smells can our noses detect?

For decades, the number that people have cited is 10,000 smells. I remember hearing this number back when I was an undergrad working on the olfactory system and wondering where it came from. Turns out, it was basically pulled out of thin air. And by thin air I mean a 1927 paper which proposed that there are four basic smells—fragrant, acid, burnt, and caprylic—that vary along a nine-point scale.^{4 }This model yields 9^{4}, or 6561, possible odors, which was soon rounded up to 10,000 and cited everywhere (such as here, here, and here).

So it’s about time that someone actually tested whether this number is anywhere close to true. The trouble is, it’s not feasible to collect samples of all the possible smells that might exist in the world, let alone to ask people how many of them smell different.

### Our senses have dimensions

For other senses like hearing, this problem is much simpler. Sounds are a combination of many different “pure tones” (basically musical notes). Sure, there are technically an infinite number of tones, but the tones vary predictably along a single axis: frequency (a.k.a. pitch). If tone A sounds lower than tone B, and B sounds lower than C, then A will sound lower than C. So in order to calculate how many different pure tones we can perceive, we mostly just need to know how different two tone frequencies must be for us to tell them apart.

The situation is similar for color vision, although color varies along three dimensions instead of just one: red, green, and blue. We can compare different colors by simply specifying how much red, green, and blue they have. Researchers have thus estimated that we can distinguish hundreds of thousands of pure tones and millions of colors.^{5-7}

The problem with olfaction is that we don’t know how many dimensions (which you can think of as independent, fundamental “categories”) our brain uses to describe a smell. In the simplest case, smell might vary along only one dimension, like “pleasantness”.^{8} This would mean that the only way we’d be able to describe a smell is by how pleasant or unpleasant it is. From experience, we know this isn’t true: smell probably has at least a handful of dimensions, like maybe fruity, pungent, woody, and so on. But some of these categories might just represent combinations of other categories. For instance, how would we know whether “lemony” is a fundamental category or just a combination of “fruity” and “sour”? So currently we have very little idea of what a fundamental odor category even means, let alone how many individual smells there are.

### Counting smells

Leslie Vosshall’s lab decided to tackle this question head-on. They started with 128 basic odors that spanned all the different odor categories they could think of. Then they prepared many mixtures of these odor components and tested whether people could tell them apart. Their data showed that two mixtures could generally be distinguished if less than 50% of their components were overlapping. The authors then calculated how many mixtures you can make from the 128 components and still have no two mixtures overlapping by more than 50%.^{9} That should represent the number of different smells we can perceive.

The number turns out to be 1.7 trillion! That sounds ridiculously high, but remember that the total number of mixtures is WAY higher: for every one of the 1.7 trillion different smells, there are 9 quadrillion smells that can’t be distinguished from it.

This paper got a lot of attention when it was published back in March. People seemed to have a new appreciation for how impressive our noses are.

### Igniting the debate

Then recently, in the last week or so, Markus Meister published a fierce rebuttal of this paper. His main point is that we don’t know how many dimensions the brain uses to describe smell, as discussed above. It turns out that Vosshall’s study makes an implicit assumption that smell has at least 128 dimensions—one for each of the original odor components. I realize this may not be intuitive, but the idea is that each component defines its own unique category of odor perception, and you need to combine all those categories to describe a smell. But we don’t know if that’s really true.

For the Vosshall analysis to be correct it actually doesn’t matter whether the 128 dimensions correspond to the 128 odor components or to other categories—but it’s essential that there are at least 128 dimensions. If not, then their estimate of a trillion smells may be way too high. Meister describes some theoretical examples to illustrate this point.

His first example asks us to imagine a bacterium that can perceive only three smells: “yum”, “yuck”, and “meh”. This bacterium might be able to smell thousands of molecules, but it can only describe them in one of those three ways. Odor mixtures would also evoke one of these three smells depending on their components. Meister then simulated the human experiments and analysis performed by Vosshall’s paper, which computed that the bacterium could sense 100 million different smells! Since we know that it really only has three smells (by design), our analysis must have gone terribly wrong.

The reason the Vosshall analysis led us astray is because it assumes that smell has many dimensions, whereas the bacterium actually perceives smell in very simple terms. The bacterium may be able to discriminate millions of pairs of smells, if each pair is presented separately, but it’s really just perceiving the same three smells over and over again. How do we know that the humans in Vosshall’s study aren’t doing something similar?

Meister’s second example, which I won’t describe in detail (see notes below if you’re interested),^{10} also highlights the importance of knowing the “dimensionality” of smell. He considers the possibility that smell varies along just one dimension, such as “pleasantness”. Under this assumption, reanalyzing the data in Vosshall’s paper calculates that we can only perceive 10 different smells. That’s a bit off from a trillion, wouldn’t you say?

### Taking sides (or not)

So who’s right? Can we really perceive a trillion smells or not?

In my view, both sides have merit. Vosshall’s paper was the first study EVER to take a stab at answering this fundamental question. The number they came up with may not be exactly right, but at least it’s a starting point. Their paper has been criticized by people who say that they’re extrapolating really big conclusions from a limited data set. But that’s the whole point! There’s no way we can physically count all the different smells; we must conduct experiments in a small corner of the odor universe and then extrapolate those results to the real world. This inherently requires making some assumptions. The question is which assumptions we should make.

I agree with Meister that a critical assumption in Vosshall’s study was not explicitly stated and may not be valid: the assumption that our brain uses at least 128 dimensions to describe smell. Meister’s examples prove that the same data can be used to get a very different answer (10 different smells instead of a trillion) if you make a very different assumption (1 dimension instead of 128).

He believes that this invalidates the paper’s results. I’m not so sure. Just because you can get different answers doesn’t mean that all answers are equally likely, because not all assumptions are equally warranted. So the real question is, how many dimensions does smell have?

Meister argues that 128 dimensions is highly implausible. But it might not be far off. As I discussed last week, our noses contain over 300 olfactory receptors. Each receptor is activated by a particular set of odors based on their chemical structure. So we could think of each receptor as representing a different dimension, or category, of smell. Even if the receptors aren’t all providing unique information (meaning that not every one counts as a separate dimension), 128 dimensions doesn’t seem so implausible in this light.

Studies from Noam Sobel’s lab have tried to experimentally address this question of dimensionality. One study estimated that 10 dimensions can only explain 75% of your perception of smell, suggesting that the true number of dimensions is higher.^{8} A different study modeled how the chemical structure of odors relates to their smell; the optimal model used 21 descriptors, which we could think of as dimensions.^{11} So I’m curious to know how many different smells the Vosshall method predicts if we were to assume that smell has something like 20 dimensions instead of 128. It may not be in the trillions, but I imagine it’s still a very high number.^{12}

### Science is a battlefield

There’s another aspect of this scientific brawl that I want to touch on. If any of you actually clicked on the link to read Meister’s paper, the first thing you probably noticed—before any of the arguments or examples or figures—is the inflammatory and hostile language. Instead of simply pointing out the potential flaws in Vosshall’s study, Meister refers to their results as “extravagant claims” that “have no basis” and “are wrong by astronomical factors”. He declares that “None of this is true” and blames their university, funding agency, and the journal for disseminating these results to the public.

These assertions are rather unfair. (“Extravagant”, you might even say.) First of all, you can’t really blame the university or anyone else for publicizing a study that was peer-reviewed and accepted. Second, Meister doesn’t have any actual proof that the paper is wrong. He may be right in questioning their assumptions, but it’s misleading for him to declare that their number—a trillion smells—is definitely wrong.

I’m totally fine with people arguing about what the data mean, how to analyze them, or what other experiments might provide a better answer. In fact, this kind of scientific debate is essential for progress. But it can always be done with respect and civility. In any case, hopefully the current argument will ultimately drive the field forward and bring us closer to understanding how we perceive the mysterious world of smell.

**Notes:**

1. Bushdid C, Magnasco MO, Vosshall LB, Keller A. Humans can discriminate more than 1 trillion olfactory stimuli. *Science *343:1370-1372 (2014).

2. Meister M. Can humans really discriminate 1 trillion odors? arXiv:1411.0165 (2014).

3. Ohloff G. *Scent and Fragrances: The Fascination of Odors and Their Chemical Perspectives.* W. Pickenhagen, Lawrence BM, Transl. Springer-Verlag, Berlin (1994).

4. Crocker EC, Henderson LF. Analysis and classification of odors: an effort to develop a workable method. *Am Perfum Essent Oil Rev* 22:325 (1927).

5. Stevens SS, Davis H. *Hearing, Its Psychology and Physiology*. Wiley, New York, p. 152–154 (1938).

6. Nickerson D, Newhall SM. A psychological color solid. *J Opt Soc. Am *33:419–422 (1943).

7. Pointer MR, Attridge GG. The number of discernible colours. *Color Res Appl* 23:52–54 (1998).

8. This paper estimates that about 30% of our perception of smell falls along the single axis of “pleasantness”:

Khan RM, Luk CH, Flinker A, Aggarwal A, Lapid H, Haddad R, Sobel N. Predicting odor pleasantness from odorant structure: pleasantness as a reflection of the physical world. *J Neurosci* 27:10015-10023 (2007).

9. Here are some details about how this number was calculated. You can envision each odor mixture as a point in a 128-dimensional odor space defined by the 128 odor components. The distance between two points reflects how many overlapping components the mixtures have. So there’s some distance threshold that represents an overlap of 50%. Now you just need to determine how many points you can fit into the 128-dimensional space without any of them being closer together than that critical distance. This can be calculated by known mathematical methods.

10. In this example we imagine that all smells fall along just one dimension, such as “pleasantness”, so the only way to compare two smells is to say which one is more pleasant. Each of the 128 odor components, as well as the odor mixtures, fall somewhere along the pleasantness scale. They can be discriminated if they are sufficiently far apart. Vosshall’s paper showed that we can distinguish two mixtures if they share fewer than 50% of their components. So Meister used this threshold to calculate how many smells we’d be able to distinguish if smell varies along just one dimension. Basically this means calculating how many smells you can fit on the pleasantness scale without any of them being too close together to tell apart. The answer was 10.

11. Snitz K, Yablonka A, Weiss T, Frumin I, Khan RM, Sobel N. Predicting odor perceptual similarity from odor structure. *PLoS Comput Biol *9:e1003184 (2013).

12. I should point out that under the 128 dimensions assumption, the Vosshall estimate of 1.7 trillion smells is actually an underestimate because they only counted odor mixtures that could be made using exactly 30 of the 128 components mixed in equal amounts. If they counted all the mixtures you could make using any number of components mixed in any arbitrary ratio, the number of different smells would be way higher. So even if they’ve overestimated the number of dimensions, their underestimation in other parts of the analysis might cancel out some of that error.