Question: How many farts are never heard by anyone?
Short answer: Unknown.
Long answer: It’s troubling to think that most farts probably go unnoticed by anyone other than the perpetrator. The smell doesn’t travel very far, and many people choose to conceal the sound.
But the Internet is full of audio recordings, which could be a deep reservoir of undiscovered farts. Perhaps they are out there, waiting to be found. Can we find them?
A similar question has been posed by the search for extraterrestrial intelligence (SETI), a project aimed at detecting signs of intelligent life elsewhere in the universe. Since we have no idea how intelligent aliens would attempt to communicate, it is not clear how we would distinguish their messages from background noise. But we do know that most artificial communication systems, like FM radio, make use of a narrow range of frequencies. So, SETI’s approach has been to search the skies for strong, narrow-band signals, usually in the radio-frequency range.
Here is a picture of the strongest candidate for an alien communication ever detected, the so-called Wow! Signal:
The signal, which was detected by a radio telescope called the Big Ear, occupied a very narrow range of frequencies (labelled as channel numbers in the plot) and lasted for a short period of time. In this regard, the Wow! Signal is similar to an extraterrestrial fart, since farts are also narrow-band, short-duration events.
We previously suggested that this aspect of farts could be used to automate their detection in audio recordings. To test this idea, we derived an audio filter for identifying potential farts, based on the fact that they have a Gaussian shape g(ω) in frequency and a decaying exponential form h(t) in time. We expressed these functions as vectors, with the Gaussian centered at 275 Hz and the temporal decay having a time constant of 250 ms. The outer product yields the matrix f=g⨂h, which is shown here:
There is an obvious similarity to the Wow! Signal shown above, which suggests an immediate similarity between the search for alien intelligence and the search for terrestrial farts.
To test our fart filter, we found an audio recording that includes music and speech. The clip concerns a possible alien invasion of the kind feared by critics of SETI, but it is otherwise unremarkable. We added a couple of farts to the original recording, to generate the following composite:
The farts can be heard at about 9 and 16 seconds into the recording. We then convolved the fart filter with the audio recording to produce the output of the filter, o(t):
Here is the output of the fart filter, applied to this recording:
The filter correctly identifies the times of occurrence for both farts (indicated by the vertical lines), although it is somewhat fooled by the speech that masks the second one. Nevertheless, setting a threshold at 0.8 safely identifies both farts in this audio segment without any false positives.
What are the applications of this new technology? One application would be to scan all existing audio recordings, SETI-style, to discover previously unnoticed farts. This would require considerable computational power. Perhaps a starting point will be to scan the available recordings of people who are suspected to be particularly flatulent, namely Katy Perry and Lyndon B. Johnson. Results will be posted as they become available.