Commentary on a comment

If you want to see a masterclass in dissecting a paper, go read Tal Yarkoni’s discussion of “The dACC is selective for pain“:

That conclusion rests almost entirely on inspection of meta-analytic results produced by Neurosynth, an automated framework for large-scale synthesis of results from thousands of published fMRI studies. And while I’ll be the first to admit that I know very little about the anterior cingulate cortex, I am probably the world’s foremost expert on Neurosynth*—because I created it.

…The basic argument L&E make is simple, and largely hangs on the following observation about Neurosynth data: when we look for activation in the dorsal ACC (dACC) in various “reverse inference” brain maps on Neurosynth, the dominant associate is the term “pain”…The blue outline in panel A is the anatomical boundary of dACC; the colorful stuff in B is the Neurosynth map for ‘dACC’…As you can see, the two don’t converge all that closely. Much of the Neurosynth map sits squarely inside preSMA territory rather than in dACC proper…That said, L&E should also have known better, because they were among the first authors to ascribe a strong functional role to a region of dorsal ACC that wasn’t really dACC at all… Much of the ongoing debate over what the putative role of dACC is traces back directly to this paper.

…Localization issues aside, L&E clearly do have a point when they note that there appears to be a relatively strong association between the posterior dACC and pain. Of course, it’s not a novel point…Of course, L&E go beyond the claims made in Yarkoni et al (2011)—and what the Neurosynth page for pain reveals—in that they claim not only that pain is preferentially associated with dACC, but that “the clearest account of dACC function is that it is selectively involved in pain-related processes.”…Perhaps the most obvious problem with the claim is that it’s largely based on comparison of pain with just three other groups of terms, reflecting executive function, cognitive conflict, and salience**. This is, on its face, puzzling evidence for the claim that the dACC is pain-selective.

etc. etc. Traditionally, this type of critique would slowly be drafted as a short rebuttal to PNAS. But isn’t this better? Look how deep the critique is, look how well everything is defined and explained. And what is stopping the authors from directly interacting with the author of the critique to really get at the problem? The only thing left is some way for pubmed or Google Scholar to link these directly to the paper.

Go read the whole thing and be learned.

How many smells can a smelly person smell? 1 trillion or 10?

Earlier this year, a paper in Science attempted to answer the question: how many smells can we actually smell? At least one trillion, they claimed. Recently, Markus Meister posted a paper on arxiv which made the bold claim that we can smell at least ten smells! Or at least that the data was just as consistent with ten smells as one trillion smells.

Let’s start with the original claim – that humans can differentiate between at least a trillion smells. These experimenters chose 128 molecules and mixed them together in differing amounts. A little bit of molecule A here, a dash of molecule B there. These delectable treats were then presented in pairs to subjects who were tasked with answering whether they were given the same delight from this perfumerie or given two different scents. By imagining these odors as balls of different smells; push them too near each other and they get all mixed up and impossible to tell apart. By keeping them just far enough apart to discriminate each ball from the other, you can position them in a space bordered in each dimension by the number of distinct odorant molecules. Count how many of them there are and you’ve got your number of smells!

Markus Meister attacks this in three fundamental ways. They are each fairly interesting in their own right and worth dissecting for what they say about perception, behavior, and the differences between vision and olfaction.

He first constructs a simple olfactory system that contains 128 primary odors and makes them repulsive or attractive. Add these up, and if you have 2 more in one direction than another and they become ‘yum’ or ‘yuck’ percepts and otherwise are ‘meh’. But then if you calculate the discriminability of the mixtures you see there are 3*10^8 discriminable odors even though there are only three percepts!

But note that he is conflating ‘perception’ with ‘discrimination’. To understand this better, let’s construct another olfactory system that only has two percepts: ‘different’ and ‘the same’.  This olfactory system takes two odors, one after the other, and compares them. If the combination of molecules that make up the odor are the same, the system says ‘the same’. If they are not then the system says ‘different’. Now we know by construction that there are only two percepts that this bacteria, this animal, this system, can sense. It can only tell you one of two things! But boy can it discriminate a lot of different odors (infinitely many, in fact).

Choose the color

There’s actually a fun test of this online. In this test, you are shown a grid of squares of the same color with one slightly different and are asked to select the unique square. As the test goes on, it gets harder and harder. Right when you get to the edge of what you can discriminate, you can often choose the correct answer even though you don’t perceive it to be different. It almost feels like magic.

The second criticism concerns the dimensionality of the sensory data. How many ways does it vary? In vision, we know that people are trichromats (for the most part). Red, blue, green: these are the three fundamental dimensions color vision varies across. How many are dimensions are there in olfaction? There are at least 400 odorant receptor genes in humans, which suggests that there are at least 400 different odorant molecules that we could detect – though the exact number depends on the wiring of the olfactory system.  This suggests that smells exist in 400 orthogonal directions in humans.

Markus Meister shows that if odors are represented along one dimension then the same analysis used in the initial paper yields ten discriminable odors. On the other hand, if you have more (non-orthogonal) dimensions, you could potential discriminate an infinite number odors. Therefore, he claims, this analysis is just plain wrong. We’ll call this the “choose your own dimension” criticism and probably has an empirical answer (which happens to be ~400)…

Update: thinking about it, there’s an analogy with the taste system. Taste has sour, sweet, bitter, etc as the dimensions, or ‘basic flavors’. What is the olfactory equivalent? I’m guessing there are a lot of them – but who knows! That’s what this particular argument is about.

sphere packing

The final criticism is that the sphere packing technique hinges on an unnoticed assumption: that each ball is distinct. But what if they weren’t? What if you could discriminate between a little and a medium amount of odor, but not a little and a lot of odor? Or what if you unique combinations of the odor were somehow perceptually the same? This could either happen through a warping of the space or dramatic nonlinearities. Does this seem likely? Probably not – but it is an empirical question. And the answer should be in the data!

So how many smells can a smelly person smell? Probably more than ten; probably more than a million. Perhaps it is hardest to simply conceptualize what it means to discriminate between millions of odors.


Bushdid, C., Magnasco, M., Vosshall, L., & Keller, A. (2014). Humans Can Discriminate More than 1 Trillion Olfactory Stimuli Science, 343 (6177), 1370-1372 DOI: 10.1126/science.1249168

Meister M (2014). Can Humans Really Discriminate 1 Trillion Odors? arXiv