Re: [AUDITORY] Frequency + Political Acoustics

[Adam Weisser <adam_weisser@xxxxxxxxxxx>]

Dear all,

Thank you to all those who have engaged with my text - this is much appreciated. The discussion about pitch seems to have gotten a life of its own, so I'm going to add my 2 cents now (have we made it to a quarter already?), before losing the thread. 

TLDR pitch: Re pitch and frequency - yes, they are definitely two different things. And it's 100% true I could have emphasized that in the case of pitch and further broken it down into the different types, which would have more clearly differentiated it from frequency. Instead, I tried to only emphasize how frequency is fundamental to all of sensation and perception and is not perceptually equivalent to either time or space. I did not make any claim about pitch here.

TLDR relativity paradox: The original paradox is not much of a paradox if we adhere to the mandatory spacetime logic, but if we associate the detection of a remote event with knowledge of a spectrum, other paradoxes may arise related to determinism.

And the answers (apologies for the length):

Pitch

My point in this work was more elementary than explaining what pitch is and how the auditory system computes (or generates) different types of pitch. Rather, a major motivation was to indicate that the most important senses we have all rely on spectrally tuned receptors (photoreceptors in vision, mechanoreceptors in touch, and hair cells in hearing and balance). After the different stimuli are transduced, their perceptual manifestation corresponds to something else that pertains to both temporal and spectral degrees of freedom of the stimulus, rather than to its temporal or spatial aspects only. In hearing we may call it pitch, in vision color, and in touch, maybe texture (does anybody know of another term?), especially when it is combined with the spatial frequency spectrum. These percepts are unique to every sensory modality and they are not equivalent to time and could hardly ever be confused with it in normal circumstances. I think we take it more or less for granted in hearing science that we have this extra spectral degree of freedom, but for some reason it appears to have been lost on physicists, to my best knowledge, who have focused strictly on space and time as fundamental types of dimensions that make our reality.

More specifically about hearing:

In general, broadband signals as are audio stimuli do not have a unique decomposition (maybe alluded to indirectly by Jan?). This has the potential to give rise to all sorts of strange perceptual effects when the outputs from differently tuned channels are compared or eventually perceptually re-synthesized, following the initial mechanical filtering and some downstream processing. In color, it would give rise to ambiguous color naming perception, for example, or to other weird color illusions that have to do with the relative color context (e.g., https://en.wikipedia.org/wiki/The_dress). But sound is arguably more complex as a signal than visible light, partly because the audio range overlaps with the fastest neural timing capabilities, which enables cross-correlation and phase locking in some conditions. Carrier phase-locking is impossible in vision, as no biological system we know of can track light-frequency phase (400-750 THz). In sound there is also significantly more variation in receptor tunings that altogether cover a broader relative bandwidth than vision (10 octaves vs. less than an octave; this enables harmonicity only in hearing). All in all, in sound there are generally more possibilities on how to extract low-level patterns, symmetries, degeneracies - signal features that can aid perception to distinguish informative inputs from completely random, feature-less sounds.

As I understand it, whether the periodicity extraction method, which is ultimately perceived as pitch, is temporal or spectral is immaterial for the more abstract question of the dimensionality of reality. If there is an extra degree of freedom in the signal in periodicity, then it would show also spectrally, because we can always transform between the two representations : autocorrelation Fourier-transforms to the power spectrum for stationary processes (Wiener-Khintchine theorem; à la Licklider's duplex theory, 1951). There is a similar relationship that holds for nonstationary (short-time) processes (à la Lyon, 2018), as are all the sounds we hear, but this invokes an instantaneous character of the periodicity (and pitch and frequency, by association), which elicits the troubling definitional paradoxes I tried to wrestle with in my text: we routinely invoke periodicity to explain reality, but nothing in reality is truly, mathematically periodic. In the Fourier world of complex unit circles that Dick and Douglas mentioned, this is tantamount to saying that there are no perfect, ideal Platonic / Aristotelian circles, although we can perceive when something gets close enough.

Andromeda paradox (sorry again, this is very long)

Sharath additionally brought up the two related paradoxes in the ability to relate to remote events that are subjected to special relativistic effects - the Rietdijk–Putnam argument and Penrose's Andromeda paradox, translated to an imaginary acoustical problem. Strictly speaking, I am not sure that my work has anything novel to say about it, although I can try my best, and if anybody understands it better, then please correct me (maybe on a separate thread?).

The argument and paradox strike me as quite different. The original argument seems to be committing an error of assigning a meaning to a three-dimensional spatial reality, which is extracted from a four-dimensional spacetime. According to special relativity theory, though, there is no meaning to space without time, and vice versa. This is equivalent to saying that there is no meaning to "here" and "now", but only to "here-now", so the very notion of simultaneity as we understand it in 3D becomes relative and, ultimately, ambiguous.

Penrose (1989) went further by introducing determinism and uncertainty to the event occurrence according to the two different observers that are co-located at a remote point in space. The two observers lie on different light cones, which means that they had different histories in terms of their trajectories in spacetime before they met. So they relate differently to the *decision* of launching the spaceship from Andromeda: it is in the past of one and in the future of the other. However, at the moment of detection of the spaceship on planet Earth, their 4D histories intersect, and they are in agreement that it has indeed arrived. That moment is deterministic by both accounts. The seeming paradox lies in the inability to form a unanimous idea for the very occurrence of an event in relative time terms: before or after. 

A three-dimensional analogy would be to try and form an agreement about the direction of tree growth on antipodal coordinates on the globe. For example, for a person in Hawaii trees grow upwards, whereas in South Africa they appear to grow downwards, if the up-down Hawaiian axis is taken as absolute. But if one travels to the other's location, they would readily agree on the direction of tree growth and acknowledge that up and down are relative and not absolute directions using a spherical metric.

My idea about the Andromeda paradox doesn't require relativity, or other complicated distance related effects (e.g., Doppler shift, dispersion). At the most basic level, I am arguing that frequency is meaningful here, because we are detecting light or sound, by generally appealing to a bandlimited measurement instrument. So the information about the event has to be registered within a spectrum of some sort. We can be more specific and ask what kind of signal we are going to accept as deterministically conveying to us that the remote spaceship launch has indeed happened (i.e., with probability equal to unity). Once we direct our detectors to the correct angle in space, we may seek a short pulse at a certain designated frequency, or frequency bandwidth, or a unique combination of several such pulses at different times and frequencies.

Ideally, we would like this confirmatory signal to be of limited duration and bandwidth. Unfortunately, we cannot have it both ways - if the signal has finite support in one domain, the reciprocal domain would be infinite (Slepian, 1976). What we regularly do, therefore, is to truncate the signal using time-windowing, as well as band-limitation. This works well in engineering, but mathematically and physically speaking it results in an improper signal. And yet, for every intent and purpose, it serves us just fine, because we do not care about the remote past and future of the signal, just as we do not care about very high frequency, ultra-low amplitude residual components of the infinite-bandwidth spectrum that we cannot measure anyway.

But now we are faced with a different question. What kind of determinism do we end up with if we are applying these signal manipulations on our observed reality? The transmission event at the remote location should have distinct start and end points, when finite energy is being injected into the otherwise constant background noise of the universe. But if energy was injected, then the transmission system is not closed, so we're not allowed to use the standard Fourier transform, which implicitly assumes energy conservation, unless we correct for that event in the complete history of the signal and rework the problem (Placharel's theorem cannot be violated). But this logic entails that the event has always been known and determined from the beginning of time, when the infinitely-long sinusoids that make its time-independent spectrum started. This is a troubling solution to accept, because it entails a totally rigid form of determinism.

If instead we choose to apply a time window on the signal (the only reasonable thing to do in practical situations), we allow for some ignorance (indeterminism) about the remote past and future of the signal and other events that occupy the same spectrum. By doing so, though, we also herald then a time-dependent spectrum that applies only to that time window. We can relate to it as parametric within the time window of choice (or the spectrogram time-bin, etc.), but it becomes more and more cumbersome the more complex the long-time signal becomes, especially if we have to follow it in real time. This is reflected in various time-frequency analytical methods (as is maybe effectuated by the ear), where time and frequency are on equal footing, more or less: if one is dimensional, it is logically inconsistent to argue that the other one isn't. So frequency here may be thought of as an additional dimension or reality, alongside time and space.

Therefore, there appears to be some tradeoff between the dimensionality of time and frequency, and (in)determinism.

Thank you and all the best,

Adam.

On Sun, Apr 13, 2025, at 8:41 PM, Douglas Scott wrote:

Hi Jan

The reason I brought up the semiotic aspect is because confusion in terminology is irreducible.

When you do a Fourier analysis you are adding your input to a periodic substrate (sine waves at various frequencies), so you can't escape the fundamental periodic nature of the analysis even if you are analysing inharmonic noise. But the *function* of Fourier analysis is to convert that periodic representation into a single "frequency" or note-name value. At that level you are perfectly correct: Saying that something is at 220Hz is fundamentally an aperiodic statement.

And you are right, when you dig into it: You can usefully still treat noisy signals as having a well defined pitch if you are careful about it and find stable patterns of representation (periodicity again), even if it  isn't immediately strictly obvious why it would make theoretical sense.

This whole process forms a semiotic cycle where you move from one type of representation to another using either periodic or static referents without a starting or stopping point. So, for example, the ear-drum is impacted by air-pressure variations (periodic) which gets transferred to the cochlea where specific hair-cells are activated (point-like in terms of position), which in turn increases the periodic firing of neurons, which results in the release of excitatory or inhibitory neurotransmitters and so forths. It can always be framed as firsts impacting seconds in terms of thirds which act as firsts. How all that amounts to conscious perception of something like "Pitch" is appropriately described as "The Hard Problem".

To come full circle on this (as it were), this type of semiotic confusion is also where political division comes from. Not only is everyone defining their terms in their own ways, but people also approach things from different levels of analysis with different functions in mind, before you even consider absurd assumptions that we all start with and forget we made. As Mendelsohn said: "It's not that music is too imprecise for words, but too precise"—The real world is far too precise to be adequately described by mere words. The only solution is to talk it through, but that requires an open forum and a presumption of good faith that is decidedly lacking in the current political discourse for various reasons, not the least of which is deliberate active disinformation campaigns from *everybody* involved along with their respective uncles. Even people who might not even be considered as players. When people are locked into a static point of view and refuse to consider their own axioms, though, any debate quickly devolves into little more than proselytisation of devoutly held beliefs along with the exercise of shibboleths and various oaths of allegiance.

Doug