this implies that humans have an intuitive sense of the shape of the waveform, which I think would be surprising!! And also empirically testable

(not saying you're wrong, but it's not necessarily obvious to me as true. The sound is a vibration/signal, how our brains interpret it may have no correlation to its "shape". Do we have an intuition for "spiky" electromagnetic signals? maybe we do, that's why looking at nature, smooth curves and such, is empirically more relaxing for people than artificial environments..?)

Higher frequencies carry more energy, also every human has a sense of waveforms. It's called "sound". Tonality and sound differentiation are deeply important to speech as well as for recognizing animals. Then there's music, of course :)

But I guess you were getting at some sort of synaesthesia?

Indeed an interesting question how that is related.

I was referring to waveforms because of the duality with sound

I think the surprising thing would be if the logic goes high frequency -> spiky waveform -> spiky shape, because that would imply that that particular representation of the sound is being used as part of the intuition. Which would be unusual, as it's not generally how people experience sound (for sure the opposite doesn't really occur: even someone very used to looking at waveforms will struggled to actually understand a sound by looking at the waveform to anywhere near the detail of listening to it). Even with synesthesia it tends to be associated with colors/feelings/smells etc in a way that doesn't tend to match with technical representation of sound.

Well how would you imagine a spiky sound from say, a synthesizer?

Guess it would have lots of overtones / not a smooth signal curve (Fourier duality)

I dont know if this is true. For example sine waves, saws and square waves are very intuitive to me. I think with graphical representation of sound the problem is that the experience of complex sounds is a 3 dimensional thing to humans.

When we talk about music, layers or tracks or whatever you want to call them always become a thing.

For the sound nerds: A spectrum representation also does not reflect how we experience sound. We humans/animals are so trained or born to distinguish sound sources by timbre. A spectrum analyser splits it on the spectrum of tones, not the spectrum of timbres, therefor it's still not a good representation.

Well we don’t hear in the time domain, we hear in the frequency domain. The neuron firing rate is too slow to sample audio. Our ear does a kind of Fourier decomposition. Still in a sense we’re hearing the waveform, just the Fourier decomposition of it.

Consider why we call some sounds "acute".

Of course we do, humans can sense timbre and transients and all that

Being able to sense timbre has nothing to do with being able to tell the shape of the waveform of a sound.

You're able to recognize red, you're unable to tell me it's wavelength (intuitively)

Recognising red _is_ recognising its wavelength. True, we don't know what frequency we hear/wavelength we see is associate with which specific number, but that's irrelevant.

Humans are born with the capability of doing a mechanical Fourier decomposition in our ears. Knowing the amplitude at each frequency, as all humans that can hear do, gives us information about the waveform.

Sensing timbre therefore is information about the waveform. We do not have complete information (e.g. we do not sense all the phase information) but we have approximate information about the time-domain waveform.

To be more specific, lots of high frequency content means we are hearing sharp transients, so quickly changing waves. Lots of low frequency content means we are hearing smoother waves

Fourier transform is a "bouba -> kikki" transform.

I think it's just that bouba has o, and kiki has k. Also the b is half-round, and I is more spiky. Visual differences, not auditory. edit: You make a round shape with your mouth in o

The article says it also works in some languages without a writing system.

I wonder what the outcome would be if they said "bouba" in a high-pitched voice, and "kiki" in a low-pitched voice.

I think it's the shapes made by your mouth and tongue to make the sounds. Rounded to make b and ou and a, and sharp corners and tongue-palate gap to make k and i. The Wikipedia article mentions a little about this.