Subject: Re: [AUDITORY] Frequency + Political Acoustics From: Adam Weisser <adam_weisser@xxxxxxxx> Date: Tue, 15 Apr 2025 01:16:49 +0300--0a032521d3314bd2a557d2243cb22f15 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Dear all, Thank you to all those who have engaged with my text - this is much appr= eciated. The discussion about pitch seems to have gotten a life of its o= wn, so I'm going to add my 2 cents now (have we made it to a quarter alr= eady?), before losing the thread.=20 TLDR pitch: Re pitch and frequency - yes, they are definitely two differ= ent 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 woul= d have more clearly differentiated it from frequency. Instead, I tried t= o only emphasize how frequency is fundamental to all of sensation and pe= rception and is not perceptually equivalent to either time or space. I d= id not make any claim about pitch here. TLDR relativity paradox: The original paradox is not much of a paradox i= f we adhere to the mandatory spacetime logic, but if we associate the de= tection 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 p= itch. Rather, a major motivation was to indicate that the most important= senses we have all rely on spectrally tuned receptors (photoreceptors i= n vision, mechanoreceptors in touch, and hair cells in hearing and balan= ce). After the different stimuli are transduced, their perceptual manife= station corresponds to something else that pertains to both temporal and= spectral degrees of freedom of the stimulus, rather than to its tempora= l or spatial aspects only. In hearing we may call it pitch, in vision co= lor, and in touch, maybe texture (does anybody know of another term?), e= specially when it is combined with the spatial frequency spectrum. These= percepts are unique to every sensory modality and they are not equivale= nt to time and could hardly ever be confused with it in normal circumsta= nces. I think we take it more or less for granted in hearing science tha= t 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 th= at 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 potent= ial to give rise to all sorts of strange perceptual effects when the out= puts from differently tuned channels are compared or eventually perceptu= ally 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 h= ave to do with the relative color context (e.g., https://en.wikipedia.or= g/wiki/The_dress). But sound is arguably more complex as a signal than v= isible light, partly because the audio range overlaps with the fastest n= eural timing capabilities, which enables cross-correlation and phase loc= king 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 recepto= r tunings that altogether cover a broader relative bandwidth than vision= (10 octaves vs. less than an octave; this enables harmonicity only in h= earing). All in all, in sound there are generally more possibilities on = how to extract low-level patterns, symmetries, degeneracies - signal fea= tures that can aid perception to distinguish informative inputs from com= pletely random, feature-less sounds.=20 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 i= s an extra degree of freedom in the signal in periodicity, then it would= show also spectrally, because we can always transform between the two r= epresentations : autocorrelation Fourier-transforms to the power spectru= m for stationary processes (Wiener-Khintchine theorem; =C3=A0 la Licklid= er's duplex theory, 1951). There is a similar relationship that holds fo= r nonstationary (short-time) processes (=C3=A0 la Lyon, 2018), as are al= l the sounds we hear, but this invokes an instantaneous character of the= periodicity (and pitch and frequency, by association), which elicits th= e troubling definitional paradoxes I tried to wrestle with in my text: w= e routinely invoke periodicity to explain reality, but nothing in realit= y is truly, mathematically periodic. In the Fourier world of complex uni= t circles that Dick and Douglas mentioned, this is tantamount to saying = that there are no perfect, ideal Platonic / Aristotelian circles, althou= gh 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 e= ffects - the Rietdijk=E2=80=93Putnam argument and Penrose's Andromeda pa= radox, 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 co= rrect me (maybe on a separate thread?). The argument and paradox strike me as quite different. The original argu= ment seems to be committing an error of assigning a meaning to a three-d= imensional spatial reality, which is extracted from a four-dimensional s= pacetime. According to special relativity theory, though, there is no me= aning to space without time, and vice versa. This is equivalent to sayin= g 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 rel= ative and, ultimately, ambiguous. Penrose (1989) went further by introducing determinism and uncertainty t= o the event occurrence according to the two different observers that are= co-located at a remote point in space. The two observers lie on differe= nt light cones, which means that they had different histories in terms o= f their trajectories in spacetime before they met. So they relate differ= ently 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 mome= nt of detection of the spaceship on planet Earth, their 4D histories int= ersect, and they are in agreement that it has indeed arrived. That momen= t is deterministic by both accounts. The seeming paradox lies in the ina= bility to form a unanimous idea for the very occurrence of an event in r= elative time terms: before or after.=20 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 Afr= ica 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 rea= dily agree on the direction of tree growth and acknowledge that up and d= own 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 b= andlimited measurement instrument. So the information about the event ha= s to be registered within a spectrum of some sort. We can be more specif= ic and ask what kind of signal we are going to accept as deterministical= ly 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 desi= gnated frequency, or frequency bandwidth, or a unique combination of sev= eral such pulses at different times and frequencies. Ideally, we would like this confirmatory signal to be of limited duratio= n and bandwidth. Unfortunately, we cannot have it both ways - if the sig= nal has finite support in one domain, the reciprocal domain would be inf= inite (Slepian, 1976). What we regularly do, therefore, is to truncate t= he signal using time-windowing, as well as band-limitation. This works w= ell in engineering, but mathematically and physically speaking it result= s in an improper signal. And yet, for every intent and purpose, it serve= s 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-l= ow 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 h= ave distinct start and end points, when finite energy is being injected = into the otherwise constant background noise of the universe. But if ene= rgy was injected, then the transmission system is not closed, so we're n= ot allowed to use the standard Fourier transform, which implicitly assum= es energy conservation, unless we correct for that event in the complete= history of the signal and rework the problem (Placharel's theorem canno= t be violated). But this logic entails that the event has always been kn= own and determined from the beginning of time, when the infinitely-long = sinusoids that make its time-independent spectrum started. This is a tro= ubling solution to accept, because it entails a totally rigid form of de= terminism. If instead we choose to apply a time window on the signal (the only reas= onable thing to do in practical situations), we allow for some ignorance= (indeterminism) about the remote past and future of the signal and othe= r events that occupy the same spectrum. By doing so, though, we also her= ald 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 cumbersom= e the more complex the long-time signal becomes, especially if we have t= o follow it in real time. This is reflected in various time-frequency an= alytical methods (as is maybe effectuated by the ear), where time and fr= equency 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 >=20 > The reason I brought up the semiotic aspect is because confusion in te= rminology is irreducible. >=20 > 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 in= harmonic noise. But the *function* of Fourier analysis is to convert tha= t periodic representation into a single "frequency" or note-name value. = At that level you are perfectly correct: Saying that something is at 220= Hz is fundamentally an aperiodic statement. >=20 > 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 se= nse. >=20 > 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 i= mpacted 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, w= hich results in the release of excitatory or inhibitory neurotransmitter= s 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 p= erception of something like "Pitch" is appropriately described as "The H= ard Problem". >=20 > To come full circle on this (as it were), this type of semiotic confus= ion is also where political division comes from. Not only is everyone de= fining their terms in their own ways, but people also approach things fr= om 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 w= ords, but too precise"=E2=80=94The real world is far too precise to be a= dequately described by mere words. The only solution is to talk it throu= gh, but that requires an open forum and a presumption of good faith that= is decidedly lacking in the current political discourse for various rea= sons, not the least of which is deliberate active disinformation campaig= ns from *everybody* involved along with their respective uncles. Even pe= ople 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, th= ough, any debate quickly devolves into little more than proselytisation = of devoutly held beliefs along with the exercise of shibboleths and vari= ous oaths of allegiance. >=20 > Doug --0a032521d3314bd2a557d2243cb22f15 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable <!DOCTYPE html><html><head><title></title><style type=3D"text/css">p.Mso= Normal,p.MsoNoSpacing{margin:0}=0Ap.MsoNormal,p.MsoNoSpacing{margin:0}=0A= p.MsoNormal,p.MsoNoSpacing{margin:0}=0Ap.MsoNormal,p.MsoNoSpacing{margin= :0}=0Ap.MsoNormal,p.MsoNoSpacing{margin:0}=0Ap.MsoNormal,p.MsoNoSpacing{= margin:0}=0Ap.MsoNormal,p.MsoNoSpacing{margin:0}</style></head><body><di= v style=3D"font-family:Arial;">Dear all,</div><div style=3D"font-family:= Arial;"><br></div><div style=3D"font-family:Arial;">Thank you to all tho= se who have engaged with my text - this is much appreciated. The discuss= ion 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 losin= g the thread. </div><div style=3D"font-family:Arial;"><br></div><di= v style=3D"font-family:Arial;">TLDR pitch: Re pitch and frequency - yes,= they are definitely two different things. And it's 100% true I could ha= ve emphasized that in the case of pitch and further broken it down into = the different types, which would have more clearly differentiated it fro= m frequency. Instead, I tried to only emphasize how frequency is fundame= ntal to all of sensation and perception and is not perceptually equivale= nt to either time or space. I did not make any claim about pitch here.<b= r></div><div style=3D"font-family:Arial;"><br></div><div style=3D"font-f= amily:Arial;">TLDR relativity paradox: The original paradox is not much = of a paradox if we adhere to the mandatory spacetime logic, but if we as= sociate the detection of a remote event with knowledge of a spectrum, ot= her paradoxes may arise related to determinism.</div><div style=3D"font-= family:Arial;"><br></div><div style=3D"font-family:Arial;">And the answe= rs (apologies for the length):</div><div style=3D"font-family:Arial;"><b= r></div><div style=3D"font-family:Arial;"><u>Pitch</u></div><div style=3D= "font-family:Arial;">My point in this work was more elementary than expl= aining what pitch is and how the auditory system computes (or generates)= different types of pitch. Rather, a major motivation was to indicate th= at the most important senses we have all rely on spectrally tuned recept= ors (photoreceptors in vision, mechanoreceptors in touch, and hair cells= in hearing and balance). After the different stimuli are transduced, th= eir perceptual manifestation corresponds to something else that pertains= to both temporal and spectral degrees of freedom of the stimulus, rathe= r than to its temporal or spatial aspects only. In hearing we may call i= t pitch, in vision color, and in touch, maybe texture (does anybody know= of another term?), especially when it is combined with the spatial freq= uency spectrum. These percepts are unique to every sensory modality and = they are not equivalent to time and could hardly ever be confused with i= t in normal circumstances. I think we take it more or less for granted i= n hearing science that we have this extra spectral degree of freedom, bu= t 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 t= ypes of dimensions that make our reality.</div><div style=3D"font-family= :Arial;"><br></div><div style=3D"font-family:Arial;">More specifically a= bout hearing:</div><div style=3D"font-family:Arial;">In general, broadba= nd signals as are audio stimuli do not have a unique decomposition (mayb= e alluded to indirectly by Jan?). This has the potential to give rise to= all sorts of strange perceptual effects when the outputs from different= ly tuned channels are compared or eventually perceptually re-synthesized= , following the initial mechanical filtering and some downstream process= ing. 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., <a href=3D"https://en.wikipedia.org/wiki/T= he_dress">https://en.wikipedia.org/wiki/The_dress</a>). But sound is arg= uably more complex as a signal than visible light, partly because the au= dio range overlaps with the fastest neural timing capabilities, which en= ables cross-correlation and phase locking in some conditions. Carrier ph= ase-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 si= gnificantly more variation in receptor tunings that altogether cover a b= roader relative bandwidth than vision (10 octaves vs. less than an octav= e; 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 di= stinguish informative inputs from completely random, feature-less sounds= . <br></div><div style=3D"font-family:Arial;"><br></div><div style=3D"fo= nt-family:Arial;">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 r= eality. If there is an extra degree of freedom in the signal in periodic= ity, 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;= =C3=A0 la Licklider's duplex theory, 1951). There is a similar relation= ship that holds for nonstationary (short-time) processes (=C3=A0 la Lyon= , 2018), as are all the sounds we hear, but this invokes an instantaneou= s 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 wo= rld of complex unit circles that Dick and Douglas mentioned, this is tan= tamount to saying that there are no perfect, ideal Platonic / Aristoteli= an circles, although we can perceive when something gets close enough.</= div><div style=3D"font-family:Arial;"><br></div><div style=3D"font-famil= y:Arial;"><br></div><div style=3D"font-family:Arial;"><u>Andromeda parad= ox (sorry again, this is very long)</u></div><div style=3D"font-family:A= rial;"><u><br></u></div><div style=3D"font-family:Arial;">Sharath additi= onally brought up the two related paradoxes in the ability to relate to = remote events that are subjected to special relativistic effects - the R= ietdijk=E2=80=93Putnam argument and Penrose's Andromeda paradox, transla= ted 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 (mayb= e on a separate thread?).<br></div><div style=3D"font-family:Arial;"><br= ></div><div style=3D"font-family:Arial;">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, whi= ch is extracted from a four-dimensional spacetime. According to special = relativity theory, though, there is no meaning to space without time, an= d 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 simultane= ity as we understand it in 3D becomes relative and, ultimately, ambiguou= s.</div><div style=3D"font-family:Arial;"><br></div><div style=3D"font-f= amily:Arial;">Penrose (1989) went further by introducing determinism and= uncertainty to the event occurrence according to the two different obse= rvers that are co-located at a remote point in space. The two observers = lie on different light cones, which means that they had different histor= ies in terms of their trajectories in spacetime before they met. So they= relate differently to the *decision* of launching the spaceship from An= dromeda: it is in the past of one and in the future of the other. Howeve= r, at the moment of detection of the spaceship on planet Earth, their 4D= histories intersect, and they are in agreement that it has indeed arriv= ed. That moment is deterministic by both accounts. The seeming paradox l= ies in the inability to form a unanimous idea for the very occurrence of= an event in relative time terms: before or after. <br></div><div s= tyle=3D"font-family:Arial;"><br></div><div style=3D"font-family:Arial;">= 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 Af= rica they appear to grow downwards, if the up-down Hawaiian axis is take= n as absolute. But if one travels to the other's location, they would re= adily agree on the direction of tree growth and acknowledge that up and = down are relative and not absolute directions using a spherical metric.<= /div><div style=3D"font-family:Arial;"><br></div><div style=3D"font-fami= ly:Arial;">My idea about the Andromeda paradox doesn't require relativit= y, or other complicated distance related effects (e.g., Doppler shift, d= ispersion). At the most basic level, I am arguing that frequency is mean= ingful here, because we are detecting light or sound, by generally appea= ling to a bandlimited measurement instrument. So the information about t= he 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 dete= rministically conveying to us that the remote spaceship launch has indee= d happened (i.e., with probability equal to unity). Once we direct our d= etectors to the correct angle in space, we may seek a short pulse at a c= ertain designated frequency, or frequency bandwidth, or a unique combina= tion of several such pulses at different times and frequencies.<br></div= ><div style=3D"font-family:Arial;"><br></div><div style=3D"font-family:A= rial;">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 tru= ncate 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, i= t 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 spectr= um that we cannot measure anyway.</div><div style=3D"font-family:Arial;"= ><br></div><div style=3D"font-family:Arial;">But now we are faced with a= different question. What kind of determinism do we end up with if we ar= e applying these signal manipulations on our observed reality? The trans= mission 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 stand= ard Fourier transform, which implicitly assumes energy conservation, unl= ess we correct for that event in the complete history of the signal and = rework the problem (Placharel's theorem cannot be violated). But this lo= gic entails that the event has always been known and determined from the= beginning of time, when the infinitely-long sinusoids that make its tim= e-independent spectrum started. This is a troubling solution to accept, = because it entails a totally rigid form of determinism.</div><div style=3D= "font-family:Arial;"><br></div><div style=3D"font-family:Arial;">If inst= ead we choose to apply a time window on the signal (the only reasonable = thing to do in practical situations), we allow for some ignorance (indet= erminism) about the remote past and future of the signal and other event= s that occupy the same spectrum. By doing so, though, we also herald the= n a time-dependent spectrum that applies only to that time window. We ca= n relate to it as parametric within the time window of choice (or the sp= ectrogram time-bin, etc.), but it becomes more and more cumbersome the m= ore complex the long-time signal becomes, especially if we have to follo= w it in real time. This is reflected in various time-frequency analytica= l 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 logica= lly inconsistent to argue that the other one isn't. So frequency here ma= y be thought of as an additional dimension or reality, alongside time an= d space.</div><div style=3D"font-family:Arial;"><br></div><div style=3D"= font-family:Arial;">Therefore, there appears to be some tradeoff between= the dimensionality of time and frequency, and (in)determinism.</div><di= v style=3D"font-family:Arial;"><br></div><div style=3D"font-family:Arial= ;">Thank you and all the best,</div><div style=3D"font-family:Arial;">Ad= am.</div><div style=3D"font-family:Arial;"><br></div><div style=3D"font-= family:Arial;"><br></div><div style=3D"font-family:Arial;"><br></div><di= v style=3D"font-family:Arial;"><br></div><div>On Sun, Apr 13, 2025, at 8= :41 PM, Douglas Scott wrote:</div><blockquote type=3D"cite" id=3D"qt" st= yle=3D""><div dir=3D"ltr"><div>Hi Jan</div><div><br></div><div>The reaso= n I brought up the semiotic aspect is because confusion in terminology i= s irreducible.</div><div><br></div><div>When you do a Fourier analysis y= ou 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 s= ingle "frequency" or note-name value. At that level you are perfectly co= rrect: Saying that something is at 220Hz is fundamentally an aperio= dic statement.</div><div><br></div><div><div>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 pattern= s of representation (periodicity again), even if it isn't immediat= ely strictly obvious why it would make theoretical sense.</div><div><br>= </div><div>This whole process forms a semiotic cycle where you move= from one type of representation to another using either periodic or sta= tic referents without a starting or stopping point. So, for example, the= ear-drum is impacted by air-pressure variations (periodic) which gets t= ransferred to the cochlea where specific hair-cells are activated&n= bsp;(point-like in terms of position), which in turn increases the perio= dic firing of neurons, which results in the release of excitatory or inh= ibitory neurotransmitters and so forths. It can always be framed as firs= ts impacting seconds in terms of thirds which act as firsts. How all tha= t amounts to conscious perception of something like "Pitch" is appropria= tely described as "The Hard Problem".</div></div><div><div><br></div><di= v>To come full circle on this (as it were), this type of semiotic confus= ion is also where political division comes from. Not only is everyone de= fining their terms in their own ways, but people also approach things fr= om 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 w= ords, but too precise"=E2=80=94The real world is far too precise to be a= dequately 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 variou= s reasons, not the least of which is deliberate active di= sinformation campaigns from *everybody* involved along with their respec= tive uncles. Even people who might not even be considered as players. Wh= en people are locked into a static point of view and refuse to cons= ider their own axioms, though, any debate quickly devolves into lit= tle more than proselytisation of devoutly held beliefs along with the ex= ercise of shibboleths and various oaths of allegiance.</div></div><div><= br></div><div>Doug</div></div></blockquote><div style=3D"font-family:Ari= al;"><br></div></body></html> --0a032521d3314bd2a557d2243cb22f15--