**Question: **How many different kinds of fart sounds are there?

**Short answer: **42

**Long answer: ** As detailed in a previous post, it is objectively quite easy to identify an individual based on the sound of his or her farts. This suggests that different fart sounds share certain similarities. In other words, even though we have recorded nearly 2000 farts, perhaps we are hearing the same sounds over and over again. If so, the total number of fart motifs might be significantly less than 2000.

Another way to ask this question is to ask about the covariance of fart sounds. That is, if you look at a bunch of sound waveforms for different farts, to what extent to the sound fluctuations follow a few common patterns? One of the most popular tools for asking this question is principal component analysis (PCA). This method takes a bunch of inputs and expresses them as combinations of a smaller number of components, sort of like the way different food recipes can be boiled down to a few ingredients. In data analysis applications, the ingredients are often called eigenvectors.

PCA has all kinds of applications, one of which is in the domain of face recognition. If you take a large database of pictures of people’s faces, PCA can extract the eigenvectors that capture most of the variation in the images, and these are called eigenfaces. By assigning a different weight to each eigenface and adding up the results, you can reconstruct images of real faces. This provides a type of data compression – rather than storing each pixel in a face image, you just need the weights (or eigenvalues) associated with each eigenface. Here are some eigenfaces that are the ingredients of most real faces:

It turns out that even a large database of face images can be distilled down to different combinations of about 43 eigenfaces.

So what about farts? We computed the eigenvectors of our 1619 fart sounds and found that farts are similar to faces. Here is the amount of variance in fart sounds that can be accounted for as different numbers of eigenfarts are combined:

We find that 95% of the variance in the 1619 farts is captured by just 42 eigenfarts, with the top 10 eigenfarts accounting for over 60%. What do these eigenfarts sound like? Here are the top 5:

One can hear the elements of many different kinds of farts in these 5 eigenfarts, which together account for about 50% of the variance in all farts.

So is it really correct to say that there are 42 different kinds of fart sounds? Not exactly. This is a bit like saying that because most cakes are made of butter and flour, there are only a few kinds of cakes. Part of the enjoyment of farts or cakes is in the variety of ways of combining ingredients and the unique contribution of each chef.