Re: A new paradigm?(On pitch and periodicity (was "correction to post")) (Peter van Hengel )


Subject: Re: A new paradigm?(On pitch and periodicity (was "correction to post"))
From:    Peter van Hengel  <pwj.vanhengel@xxxxxxxx>
Date:    Wed, 21 Sep 2011 12:21:30 +0200
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--0016e65c8a628e7ed404ad70f091 Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable Dear dr Heerens and list-members, I hesitate to get involved in this discussion as I have tried to explain th= e hydrodynamics behind (transmission line) cochlea models before in another thread on this list and don't like repeating myself. But I feel I have to lend my support the comments made by Dick Lyon. As I have stated before fluid physics states that a fluid domain (such as the cochlea or a pond) with a flexible boundary subject to a restoring forc= e (such as the aochlear partition or the pond surface) MUST exhibit 'ripples' on the surface. In the cochlea these are refered to as traveling waves. The wave energy is not traveling in the boundary itself but in the fluid. Any attempts to prove that such waves do not exist, or are based on 'bad physics', are unfortunately based on a lack of understanding of the fluid mechanics. Whether the traveling wave is the only mechanism responsible for transporting sound energy to the hair cells is still a valid question, but untill an alternative model produces similar or better results on modeling physiological, pshychophysical and OAE date, I'll stick with the transmission line. Things like pitch perception and the missing fundamental can perhaps not be explained purely by looking at the average excitation caused by the traveling wave, but I don't think anyone ever claimed they could. In my opinion it is good to develop new theories, but w= e should attempt to integrate them with existing ones instead of throwing awa= y something that has proven to work. Kind regards, Peter van Hengel 2011/9/19 Willem Christiaan Heerens <heerens1@xxxxxxxx> > Dear Dick Lyon, > > > Thank you for your substantial list of comments. Of course I will reply. > With pleasure. > > You wrote: > **Sometimes it's hard to get a reaction when you are trying to replace a > paradigm, as the silence here illustrates. I didn't really get into the > new ideas of your book much, but I have some comments on the introductory > material about why you reject the current paradigm.** > > Your reaction in the first sentence is pretty well familiar to me. It is > entirely in accordance with the procedure described by Thomas Kuhn in his > world famous 1962 essay: > > =93The Structure of Scientific Revolutions=94 > > Besides that: a former colleague of mine, a highly skilled senior profess= or > in applied physics, who reviewed our booklet during a contribution > procedure for a scientific journal, quite recently gave us the verdict th= at > he fully agreed with our arguments and statements and he urged the editor > to make a full scientific discussion possible for our views. He also warn= ed > me that to be in right is not the same as to be put in right. I myself > don=92t see all this as a problematic issue. It=92s part of the way messe= ngers > or designers of new paradigms are encountered by the mayor supporters of > the competing one. Of course the scientific reputation rankings of so man= y > scientists are involved and in danger in case a paradigm shift is > happening. > > The only issue that counts for me is that scientific arguments from both > sides brought in discussion, verified and weighted in a careful way must > turn the balance. Ignoring irrefutable arguments because they form a thre= ad > for the ranking of a scientist has always been contra productive for the > progress in a field of science. History shows many of such examples. One = of > the most salient among them certainly is the Copernican revolution. > > The result of the second line of your comment I really regret, because in > the rest of your writings I clearly can see that you have apparently > missed, misread or misinterpreted a number of issues on cardinal points. > > Let me discuss your next comment: > > **You discuss and reject two wave concepts: first, the pressure sound wav= e > that travels so fast that wavelengths will always be long compared to the > size of the cochlea, and second, "capillary" or "interfacial" waves, > presumably meaning those water surface waves where gravity provides the > restoring force. Of course, neither of these can be the explanation for > how the cochlea works.** > > I don=92t reject the pressure sound wave concept, at least not in general= . It > is of course the vehicle of mechanical vibration energy and therefore als= o > acoustical vibration energy. How could an academic physics scientist reje= ct > that? > What I have argued is that for all the frequencies that can be sensed in > the cochlea even up to 20 kHz counts that the sound velocity in perilymph= =96 > being 1500 m/s =96 in relation with these frequencies result in a wave le= ngth > always larger than 75 mm. > So therefore this mechanism cannot contribute to a discriminating mechani= sm > for frequency selectivity based on traveling waves. > > And regarding the "capillary" or "interfacial" waves I reject: yes indee= d > in quite a number of textbooks I see the comparison of the propagation of > surface waves in a pond with the slow waves inside the cochlea. It simply > is an erroneous analogon. None of the parameters necessary for the > existence of capillary waves can be found inside the cochlea. So neither > they can play a role in evoking traveling waves that have short > wavelengths. > > You wrote: > > **You also attribute to Lighthill some strange wrong ideas about > transmission lines only being able to transmit energy near their resonanc= e. > ** > > Can you be more specific? The only lines I describe are the lines in Fig= . > 1. That figure is a reproduction of the figure in Lighthill=92s paper: > > Lighthill MJ. (1981) Energy flow in the cochlea. J Fluid Mech 106: 149-21= 3. > > I haven=92t attributed strange wrong ideas to Lighthill. I have studied > carefully all the 64 pages of his paper. > > He starts with a very informative series of premises and I cite this part= : > > *** With moderate acoustic stimuli, measurements of basilar-membrane > vibration (especially, those using a M=F6ssbauer source attached to the > membrane) demonstrate: > (i) a high degree of asymmetry, in that the response to a pure tone falls > extremely sharply above the characteristic frequency, although much more > gradually below it; > (ii) a substantial phase-lag in that response, and one which increases > monotonically tip to the characteristic frequency; > (iii) a response to a 'click' in the form of a delayed 'ringing' > oscillation at the characteristic frequency, which persists for around 20 > cycles. > This paper uses energy-flow considerations to identify which features in = a > mathe=ACmatical model of cochlear mechanics are necessary if it is to > reproduce these experi=ACmental findings. > The response (iii) demands a travelling-wave model which incorporates an > only lightly damped resonance. Admittedly, waveguide systems including > resonance are described in classical applied physics. However, a classica= l > waveguide resonance reflects a travelling wave, thus converting it into a > standing wave devoid of the substantial phase-lag (ii); and produces a lo= w- > frequency cut-off instead of the high =96frequency cut-off (i). > By contrast, another general type of travelling-wave system with resonanc= e > has become known more recently; initially, in a quite different context > (physics of the atmosphere). This is described as critical-layer resonanc= e, > or else (because the reso=ACnance absorbs energy) critical-layer absorpt= ion. > It yields a high-frequency cut-off; but, above all, it is characterized b= y > the properties of the energy flow velocity. This falls to zero very steep= ly > as the point of resonance is approached; so that wave energy flow is > retarded drastically, giving any light damping which is present an > unlimited time in which to dissipate that energy. > Existing mathematical models of cochlear mechanics, whether using one-, > two- > or three-dimensional representations of cochlear geometry, are analysed > from this standpoint. All are found to have been successful (if only ligh= t > damping is incorporated, as (iii) requires) when and only when they > incorporate critical-layer absorption. This resolves the paradox of why > certain grossly unrealistic one-dimensional models can give a good > prediction of cochlear response; it is because they incorporate the one > dimensional feature of critical-layer absorption.*** > > Apparently Lighthill has never considered the possibility that the observ= ed > movements of the basilar membrane could be caused by another phenomenon > than a sound energy transporting traveling wave. > > Your next remark: > > **Actually, he showed the opposite: that a sinusoidal wave will propagat= e > until the point where the transmission line resonance gets low enough to > match the wave frequency, and at that point it will slow down to zero > velocity and die out. This is not exactly how the cochlea works (the BM = is > not very resonant), but not a bad concept from base to near the best > place.** > > You say it clearly enough: =91It isn=92t a bad concept from base to nea= r the > best place.=92 > So not having an exact agreement between theory and practice makes the > underlying hypothesis directly vulnerable for falsification. > > Indeed the cochlea cannot react like that. And I want to make this clear = by > the following series of experiments: > > Entirely based on the premises of the new paradigm I have described, I no= w > have calculated a number of predictable sound phenomena by using the > following frequencies together with prescribed phase relations in a > standard summation procedure to compose a Fourier series: > > 1: > 10000 + 10004 + 10008 + 10012 + 10016 + 10020 + 10024 Hz > Where all the contributions are sine functions. > > Our paradigm predicts: an undisputable beat of 4 Hz in a high beep tone. > > 2: > 10000 + 10004 + 10008 + 10012 + 10016 + 10020 + 10024 Hz > Where the contributions are successively alternating sine and > cosine functions. > > Our paradigm now predicts: an undisputable beat of 8 Hz in the same high > beep tone. > > 3: > 10000 + 10004.0625 + 10008 + 10012.0625 + 10016 + 10020.0625 + > 10024 Hz > Where all the contributions are sine functions. > > Our paradigm now predicts: a beep, in which an undisputable beat exists > that changes every 8 seconds from clearly 4 Hz to 8 Hz and then reverses > again to 4 Hz. So the beat pattern has a period of 8 seconds caused by th= e > systematic mistuning of 1/16 =3D 0.0625 Hz. > > Additional changes in the mistuning, like for instance from 10004.0625 in= to > 10003.9375 Hz, of either one, two or three of the mistuned frequencies ar= e > predicted to give the same results in the beat pattern as experiment 3. > > And actually I want to urge everybody to download the software program of > Yves Mangelinckx with which these sound complexes can be properly > calculated in the form of wav files from the following site: > > http://www.a3ccm-apmas-eakoh.be/a3ccm-apmas-eakoh-index.htm > > [ NOTE: The standard setting in the 1/f mode in this software program > takes care that all the individually primary calculated frequencies > contribute equal energy to the resulting sound pressure signal. This > condition is very important for the influences on pitch calculations in > case higher values of the differences between contributing frequencies > exist. ] > > This in order to give the interested reader the opportunity to falsify or= =96 > in case our predictions are correct =96 to verify our findings. > > And of course I wouldn=92t have given these examples if I wasn=92t sure o= f my > statements. > I can already inform you that verification will be the result. > > If you carry out the same series of experiments with a start frequency of > 1000 Hz instead of 10000 Hz, you will hear the same series of beat > phenomena, but now with the lower beep of the 1012 Hz instead of the 1001= 2 > Hz beep. > Even if you go down with the start frequency to 200 Hz or 400 Hz you will > still hear the same beat phenomena, but now with the low humming tone of > 200 Hz respectively with the one octave higher humming tone of 400 Hz. > > Hence it is a perception phenomenon that appears all over the entire > auditory frequency range. > > And it must be remarked that according to the current hearing theory all > the used frequencies =96 especially in the higher frequencies like in the > 10000 Hz experiments =96 according to auditory experts, and also supporte= d by > Lighthill, will propagate by means of a traveling wave to one and the sam= e > location on the basilar membrane. > > If we then still follow the current hearing paradigm, we have to believe > that the medley of that seven totally unresolved frequencies will be > transferred via one and the same nerve fiber to a location in the auditor= y > cortex, where finally out of this =91Gordian knot of stimuli=92 a beep wi= th the > described and also heard beat patterns will be reconstructed. > > Once these beat phenomena are verified as really existing for every > listener with a reasonable normal hearing, do you agree with me that for > the current paradigm this is a very serious anomaly? > In my opinion forcing an explanation within the framework of the current > paradigm will result in such a complexity that the general rule in scienc= e, > known as =91Ockham=92s Razor=92, to strive to an optimum in simplicity w= ill be > strongly violated. > > Your next remark: > > **You conclude that "the existence of two sound energy transport phenomen= a > with different transfer velocities within this tiny cochlear volume of > perilymph fluid as suggested by Lighthill is impossible." Yet all > observations do see a slow wave, much slower than the speed of sound, and > basic mathematical physics of the same sort that has been working well fo= r > over 100 years to describe waves in fluids predicts exactly that behavior= . > Some may quibble that it has not been conclusively proved that the observ= ed > slow wave carries energy; but no workable alternative has been put forwar= d, > and no experiment convincingly contradicts this main hypothesis of the > current paradigm, as far as I know. I know some on this list will probab= ly > say I'm wrong, now that I've opened the door.** > > Do you agree with me that the perilymph inside the cochlear duct, existin= g > of scala vestibuli and scala tympani, is just moving back and forth over > distances not exceeding a few micrometer? > > If you admit this fact, you should also agree with me that all the known > and involved physical quantities and parameters indicate that we are > confronted here with the problem to find the hydrodynamic solution for th= e > non-stationary small movements of an incompressible non-viscous fluid in = a > tiny narrow duct. > According to the rules of physics it is then permitted without any > additional constraints to use the non-stationary Bernoulli equation. > > The exact and detailed solution of this equation I can =96 if you wish = =96 send > you separately. > > The result is exactly the mathematical expression I have used in the > booklet: the pressure decrease in the perilymph duct in front of the > basilar membrane is everywhere proportional to the perilymph velocity > squared. > What leads to the overall result that the pressure stimulus on the basila= r > membrane is proportional to the sound energy stimulus offered to the ear. > > You further wrote: > > **Yet all observations do see a slow wave, much slower than the > speed of sound.** > > Indeed, an observation of a =91slow wavy movement=92 and the only place w= here > we can observe this is the basilar membrane. > > It isn=92t the occurrence of a wavy movement phenomenon that we have to > discuss. It is the origin of that =91traveling wave=92 that we have to > discover. Is it a vibration energy transporting wave or is it a phase wav= e, > originated out of the manner in which the resonators in the basilar > membrane are grouped? > > By the way, that is also =96 but not in an extended way =96 explained in = our > booklet. In that chapter of the booklet I describe why those =91waves=92 = always > run from base to apex. It is conform to the peculiar mechanics of the > basilar membrane system that this phase wave behavior is prescribed as it > is. > And that mathematical solution for this mechanics problem of resonators = =96 > in case of the logarithmical frequency distribution, low near the apex to > high near the base =96 can be calculated, as I have done, analytically fo= r a > pure sinusoidal tone, which exactly results in a tonotopical symmetrical > envelope of that running phase wave with center frequency equal to the > corresponding resonance frequency. > And the running direction of that phase wave is always from base to apex. > Exactly as Tianying Ren has reported in his then speech making paper that= I > have cited: > > Ren T. (2002) Longitudinal pattern of basilar membrane vibration in the > sensitive cochlea. Proc Nat Acad Sci USA 99: 17101-6. > > The animation of such a phase wave can be seen in: > > http://www.a3ccm-apmas-eakoh.be/aobmm/bm-movement.htm > > You wrote: > > **It sounds like you're trying to get away from a Helmholtz-like concepti= on > of resonators or places responding to frequencies, and replace it with a > more time-domain approach that works for a lot of pitch phenomena. But i= t > will work better to put that time-domain mechanisms AFTER the what the > cochlea does. Each hair cell is a "tap" on the BM, reporting a time-doma= in > waveform as filtered by the traveling-wave mechanism; that's where the > pitch-processing nonlinear time-domain operations start...** > > As you already have indicated in the beginning, you haven=92t studied the > booklet entirely. I know for sure that by not studying the booklet > entirely, you have drawn premature conclusions here. > > It is quite on the contrary. I think that I have explained clearly enough > in the booklet that everywhere along the basilar membrane very local > resonance with a high quality factor takes place. However not on the > primary sound pressure signal, but on the sound energy signal. Next to th= at > the basilar membrane will react everywhere =96 but not in a resonance mod= e > and therefore with much smaller displacements =96 and will show a respons= e on > other frequency components, including utmost low frequencies even until > stationary pressure signals. > > And for the explanation of our hearing sense I don=92t need a time domain > mechanism at all. > In the new paradigm, described by me, from all the distinguishable > frequencies next of course to their frequency also their individual > amplitude and phase are transmitted to the auditory cortex. > > Our brain can directly compare the entire frequency selected sound energy > stimulus with patterns that are stored in our memory. > > Actually I cannot imagine a much more simpler and faster way. > > Finally about the definition of Ockham=92s Razor =96 also spelled Occam = =96 I > found on the Internet the following physics educational website: > > http://math.ucr.edu/home/baez/physics/General/occam.html > > where among others a number of stronger but clear definitions are given, > and I cite: > > *** If you have two theories that both explain the observed facts, then y= ou > should use the simplest until more evidence comes along. > > The simplest explanation for some phenomenon is more likely to be accurat= e > than more complicated explanations. > > If you have two equally likely solutions to a problem, choose the simples= t. > > The explanation requiring the fewest assumptions is most likely to be > correct. > > . . .or in the only form that takes its own advice. . . > > Keep things simple! *** > > Within this framework I am convinced that I have done my utmost best. > > So I am awaiting for a much better explanation for the described beat > phenomena based on the current hearing paradigm. > > > Kind regards, > > Pim Heerens > --0016e65c8a628e7ed404ad70f091 Content-Type: text/html; charset=windows-1252 Content-Transfer-Encoding: quoted-printable <div>Dear dr Heerens and list-members,</div> <div>=A0</div> <div>I hesitate to get involved in this discussion as I have tried to expla= in the hydrodynamics behind (transmission line) cochlea models before in an= other thread on this list and don&#39;t like repeating myself. But I feel I= have to lend my support the comments made by Dick Lyon.</div> <div>As I have stated before fluid physics states that a fluid domain (such= as the cochlea or a pond) with a flexible boundary subject to a restoring = force (such as the aochlear partition or the pond surface) MUST exhibit &#3= 9;ripples&#39; on the surface. In the cochlea these are refered to as trave= ling waves. The wave energy is not traveling in the boundary itself but in = the fluid. Any attempts to prove that such waves do not exist, or are based= on &#39;bad physics&#39;, are unfortunately based on a lack of understandi= ng of the=A0fluid mechanics.</div> <div>Whether the traveling wave is the only mechanism responsible for trans= porting sound energy to the hair cells is still a valid question, but until= l an alternative model produces similar or better results on modeling physi= ological, pshychophysical and OAE date, I&#39;ll stick with the transmissio= n line. Things=A0like pitch perception and the=A0missing fundamental=A0can = perhaps not=A0be explained purely by looking at the average excitation caus= ed by the traveling wave, but I don&#39;t think anyone ever claimed they co= uld.=A0In my opinion it is good to develop new theories, but we should atte= mpt to integrate them with existing ones instead of throwing away something= that has proven to work.</div> <div>=A0</div> <div>Kind regards,</div> <div>Peter van Hengel<br><br></div> <div class=3D"gmail_quote">2011/9/19 Willem Christiaan Heerens <span dir=3D= "ltr">&lt;<a href=3D"mailto:heerens1@xxxxxxxx">heerens1@xxxxxxxx</a>&gt;<= /span><br> <blockquote style=3D"BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex= ; PADDING-LEFT: 1ex" class=3D"gmail_quote">Dear Dick Lyon,<br><br><br>Thank= you for your substantial list of comments. =A0Of course I will reply.<br>W= ith pleasure.<br> <br>You wrote:<br>**Sometimes it&#39;s hard to get a reaction when you are = trying to replace a<br> <div class=3D"im">paradigm, as the silence here illustrates. =A0I didn&#39;= t really get into the<br>new ideas of your book much, but I have some comme= nts on the introductory<br></div>material about why you reject the current = paradigm.**<br> <br>Your reaction in the first sentence is pretty well familiar to me. It i= s<br>entirely in accordance with the procedure described by Thomas Kuhn in = his<br>world famous 1962 =A0essay:<br><br>=93The Structure of Scientific Re= volutions=94<br> <br>Besides that: a former colleague of mine, a highly skilled senior profe= ssor<br>in applied physics, who reviewed our booklet during a contribution<= br>procedure for a scientific journal, quite recently gave us the verdict t= hat<br> he fully agreed with our arguments and statements and he urged the editor<b= r>to make a full scientific discussion possible for our views. He also warn= ed<br>me that to be in right is not the same as to be put in right. I mysel= f<br> don=92t see all this as a problematic issue. It=92s part of the way messeng= ers<br>or designers of new paradigms are encountered by the mayor supporter= s of<br>the competing one. Of course the scientific reputation rankings of = so many<br> scientists are involved and in danger in case a paradigm shift is<br>happen= ing.<br><br>The only issue that counts for me is that scientific arguments = from both<br>sides brought in discussion, verified and weighted in a carefu= l way must<br> turn the balance. Ignoring irrefutable arguments because they form a thread= <br>for the ranking of a scientist has always been contra productive for th= e<br>progress in a field of science. History shows many of such examples. O= ne of<br> the most salient among them certainly is the Copernican revolution.<br><br>= The result of the second line of your comment I really regret, because in<b= r>the rest of your writings I clearly can see that you have apparently<br> missed, misread or misinterpreted a number of issues on cardinal points.<br= ><br>Let me discuss your next comment:<br><br>**You discuss and reject two = wave concepts: first, the pressure sound wave<br> <div class=3D"im">that travels so fast that wavelengths will always be long= compared to the<br>size of the cochlea, and second, &quot;capillary&quot; = or &quot;interfacial&quot; waves,<br>presumably meaning those water surface= waves where gravity provides the<br> restoring force. =A0Of course, neither of these can be the explanation for<= br></div>how the cochlea works.**<br><br>I don=92t reject the pressure soun= d wave concept, at least not in general. It<br>is of course the vehicle of = mechanical vibration energy and therefore also<br> acoustical vibration energy. How could an academic physics scientist reject= <br>that?<br>What I have argued is that for all the frequencies that can be= sensed in<br>the cochlea even up to 20 kHz counts that the sound velocity = in perilymph =96<br> being 1500 m/s =96 in relation with these frequencies result in a wave leng= th<br>always larger than 75 mm.<br>So therefore this mechanism cannot contr= ibute to a discriminating mechanism<br>for frequency selectivity based on t= raveling waves.<br> <br>And regarding the =A0&quot;capillary&quot; or &quot;interfacial&quot; w= aves I reject: yes indeed<br>in quite a number of textbooks I see the compa= rison of the propagation of<br>surface waves in a pond with the slow waves = inside the cochlea. It simply<br> is an erroneous analogon. None of the parameters necessary for the<br>exist= ence of capillary waves can be found inside the cochlea. So neither<br>they= can play a role in evoking traveling waves that have short wavelengths.<br= > <br>You wrote:<br><br>**You also attribute to Lighthill some strange wrong = ideas about<br> <div class=3D"im">transmission lines only being able to transmit energy nea= r their resonance.<br></div>**<br><br>Can you be more specific? =A0The only= lines I describe are the lines in Fig.<br>1. That figure is a reproduction= of the figure in Lighthill=92s paper:<br> <br>Lighthill MJ. (1981) Energy flow in the cochlea. J Fluid Mech 106: 149-= 213.<br><br>I haven=92t attributed strange wrong ideas to Lighthill. I have= studied<br>carefully all the 64 pages =A0of his paper.<br><br>He starts wi= th a very informative series of premises and I cite this part:<br> <br>*** With moderate acoustic stimuli, measurements of basilar-membrane<br= >vibration (especially, those using a M=F6ssbauer source attached to the<br= >membrane) demonstrate:<br>(i) a high degree of asymmetry, in that the resp= onse to a pure tone falls<br> extremely sharply above the characteristic frequency, although much more<br= >gradually below it;<br>(ii) a substantial phase-lag in that response, and = one which increases<br>monotonically tip to the characteristic frequency;<b= r> (iii) a response to a &#39;click&#39; in the form of a delayed &#39;ringing= &#39;<br>oscillation at the characteristic frequency, which persists for ar= ound 20<br>cycles.<br>This paper uses energy-flow considerations to identif= y which features in a<br> mathe=ACmatical model of cochlear mechanics are necessary if it is to<br>re= produce these experi=ACmental findings.<br>The response (iii) demands a tra= velling-wave model which incorporates an<br>only lightly damped resonance. = Admittedly, waveguide systems including<br> resonance are described in classical applied physics. However, a classical<= br>waveguide resonance reflects a travelling wave, thus converting it into = a<br>standing wave devoid of the substantial phase-lag (ii); and produces a= low-<br> frequency cut-off instead of the high =96frequency cut-off (i).<br>By contr= ast, another general type of travelling-wave system with resonance<br>has b= ecome known more recently; initially, in a quite different context<br>(phys= ics of the atmosphere). This is described as critical-layer resonance,<br> or else (because the reso=ACnance =A0absorbs energy) critical-layer absorpt= ion.<br>It yields a high-frequency cut-off; but, above all, it is character= ized by<br>the properties of the energy flow velocity. This falls to zero v= ery steeply<br> as the point of resonance is approached; so that wave energy flow is<br>ret= arded drastically, giving any light damping which is present an<br>unlimite= d time in which to dissipate that energy.<br>Existing mathematical models o= f cochlear mechanics, whether using one-, two-<br> =A0or three-dimensional representations of cochlear geometry, are analysed<= br>from this standpoint. All are found to have been successful (if only lig= ht<br>damping is incorporated, as (iii) requires) when and only when they<b= r> incorporate critical-layer absorption. This resolves the paradox of why<br>= certain grossly unrealistic one-dimensional models can give a good<br>predi= ction of cochlear response; it is because they incorporate the one<br>dimen= sional feature of critical-layer absorption.***<br> <br>Apparently Lighthill has never considered the possibility that the obse= rved<br>movements of the basilar membrane could be caused by another phenom= enon<br>than a sound energy transporting traveling wave.<br><br>Your next r= emark:<br> <br>**Actually, he showed the opposite: =A0that a sinusoidal wave will prop= agate<br> <div class=3D"im">until the point where the transmission line resonance get= s low enough to<br>match the wave frequency, and at that point it will slow= down to zero<br>velocity and die out. =A0This is not exactly how the cochl= ea works (the BM is<br> not very resonant), but not a bad concept from base to near the best<br>pla= ce.**<br><br></div>You say it clearly enough: =A0 =91It isn=92t a bad conce= pt from base to near the<br>best place.=92<br>So not having an exact agreem= ent between theory and practice makes the<br> underlying hypothesis directly vulnerable for falsification.<br><br>Indeed = the cochlea cannot react like that. And I want to make this clear by<br>the= following series of experiments:<br><br>Entirely based on the premises of = the new paradigm I have described, I now<br> have calculated a number of predictable sound phenomena by using the<br>fol= lowing frequencies together with prescribed phase relations in a<br>standar= d summation procedure to compose a Fourier series:<br><br>1:<br>=A0 =A0 =A0= =A0 =A0 =A010000 + 10004 + 10008 + 10012 + 10016 + 10020 + 10024 Hz<br> =A0 =A0 =A0 =A0 =A0 =A0 Where all the contributions are sine functions.<br>= <br>Our paradigm predicts: =A0an undisputable beat of 4 Hz in a high beep t= one.<br><br>2:<br>=A0 =A0 =A0 =A0 =A0 =A010000 + 10004 + 10008 + 10012 + 10= 016 + 10020 + 10024 Hz<br> =A0 =A0 =A0 =A0 =A0 =A0Where the contributions are successively alternating= sine and<br>cosine functions.<br><br>Our paradigm now predicts: =A0an undi= sputable beat of 8 Hz in the same high<br>beep tone.<br><br>3:<br>=A0 =A0 = =A0 =A0 =A0 =A010000 + 10004.0625 + 10008 + 10012.0625 + 10016 + 10020.0625= +<br> 10024 Hz<br>=A0 =A0 =A0 =A0 =A0 =A0Where all the contributions are sine fun= ctions.<br><br>Our paradigm now predicts: =A0a =A0beep, in which an undispu= table beat exists<br>that changes every 8 seconds from clearly 4 Hz to 8 Hz= and then reverses<br> again to 4 Hz. So the beat pattern has a period of 8 seconds caused by the<= br>systematic mistuning of 1/16 =3D 0.0625 Hz.<br><br>Additional changes in= the mistuning, like for instance from 10004.0625 into<br>10003.9375 Hz, of= either one, two or three of the mistuned frequencies are<br> predicted to give the same results in the beat pattern as experiment 3.<br>= <br>And actually I want to urge everybody to download the software program = of<br>Yves Mangelinckx =A0with which these sound complexes can be properly<= br> calculated in the form of wav files from the following site:<br><br><a href= =3D"http://www.a3ccm-apmas-eakoh.be/a3ccm-apmas-eakoh-index.htm" target=3D"= _blank">http://www.a3ccm-apmas-eakoh.be/a3ccm-apmas-eakoh-index.htm</a><br> <br>[ NOTE: =A0 =A0The standard setting in the 1/f mode in this software pr= ogram<br>takes care that all the individually primary calculated frequencie= s<br>contribute equal energy to the resulting sound pressure signal. This<b= r> condition is very important for the influences on pitch calculations in<br>= case higher values of the differences between contributing frequencies<br>e= xist. ]<br><br>This in order to give the interested reader the opportunity = to falsify or =96<br> in case our predictions are correct =96 to verify our findings.<br><br>And = of course I wouldn=92t have given these examples if I wasn=92t sure of my<b= r>statements.<br>I can already inform you that verification will be the res= ult.<br> <br>If you carry out the same series of experiments with a start frequency = of<br>1000 Hz instead of 10000 Hz, you will hear the same series of beat<br= >phenomena, but now with the lower beep of the 1012 Hz instead of the 10012= <br> Hz beep.<br>Even if you go down with the start frequency to 200 Hz or 400 H= z you will<br>still hear the same beat phenomena, but now with the low humm= ing tone of<br>200 Hz respectively with the one octave higher humming tone = of 400 Hz.<br> <br>Hence it is a perception phenomenon that appears all over the entire<br= >auditory frequency range.<br><br>And it must be remarked that according to= the current hearing theory all<br>the used frequencies =96 especially in t= he higher frequencies like in the<br> 10000 Hz experiments =96 according to auditory experts, and also supported = by<br>Lighthill, will propagate by means of a traveling wave to one and the= same<br>location on the basilar membrane.<br><br>If we then still follow t= he current hearing paradigm, we have to believe<br> that the medley of that seven totally unresolved frequencies will be<br>tra= nsferred via one and the same nerve fiber to a location in the auditory<br>= cortex, where finally out of this =91Gordian knot of stimuli=92 a beep with= the<br> described and also heard beat patterns will be reconstructed.<br><br>Once t= hese beat phenomena are verified as really existing for every<br>listener w= ith a reasonable normal hearing, do you agree with me that for<br>the curre= nt paradigm this is a very serious anomaly?<br> In my opinion forcing an explanation within the framework of the current<br= >paradigm will result in such a complexity that the general rule in science= ,<br>known as =A0=91Ockham=92s Razor=92, to strive to an optimum in simplic= ity will be<br> strongly violated.<br><br>Your next remark:<br><br>**You conclude that &quo= t;the existence of two sound energy transport phenomena<br> <div class=3D"im">with different transfer velocities within this tiny cochl= ear volume of<br>perilymph fluid as suggested by Lighthill is impossible.&q= uot; =A0Yet all<br>observations do see a slow wave, much slower than the sp= eed of sound, and<br> basic mathematical physics of the same sort that has been working well for<= br>over 100 years to describe waves in fluids predicts exactly that behavio= r.<br>Some may quibble that it has not been conclusively proved that the ob= served<br> slow wave carries energy; but no workable alternative has been put forward,= <br>and no experiment convincingly contradicts this main hypothesis of the<= br>current paradigm, as far as I know. =A0I know some on this list will pro= bably<br> </div>say I&#39;m wrong, now that I&#39;ve opened the door.**<br><br>Do you= agree with me that the perilymph inside the cochlear duct, existing<br>of = scala vestibuli and scala tympani, is just moving back and forth over<br> distances not exceeding a few micrometer?<br><br>If you admit this fact, yo= u should also agree with me that all the known<br>and involved physical qua= ntities and parameters indicate that we are<br>confronted here with the pro= blem to find the hydrodynamic solution for the<br> non-stationary small movements of an incompressible non-viscous fluid in a<= br>tiny narrow duct.<br>According to the rules of physics it is then permit= ted without any<br>additional constraints to use the non-stationary Bernoul= li equation.<br> <br>The exact and detailed solution of this equation I can =96 if you wish = =96 send<br>you separately.<br><br>The result is exactly the mathematical e= xpression I have used in the<br>booklet: =A0the pressure decrease in the pe= rilymph duct in front of the<br> basilar membrane is everywhere proportional to the perilymph velocity<br>sq= uared.<br>What leads to the overall result that the pressure stimulus on th= e basilar<br>membrane is proportional to the sound energy stimulus offered = to the ear.<br> <br>You further wrote:<br><br>=A0 =A0 =A0 =A0 =A0 **Yet all observations do= see a slow wave, much slower than the<br>speed of sound.**<br><br>Indeed, = an observation of a =91slow wavy movement=92 and the only place where<br>we= can observe this is the basilar membrane.<br> <br>It isn=92t the occurrence of a wavy movement phenomenon that we have to= <br>discuss. It is the origin of that =91traveling wave=92 that we have to<= br>discover. Is it a vibration energy transporting wave or is it a phase wa= ve,<br> originated out of the manner in which the resonators in the basilar<br>memb= rane are grouped?<br><br>By the way, that is also =96 but not in an extende= d way =96 explained in our<br>booklet. In that chapter of the booklet I des= cribe why those =91waves=92 always<br> run from base to apex. It is conform to the peculiar mechanics of the<br>ba= silar membrane system that this phase wave behavior is prescribed as it<br>= is.<br>And that mathematical solution for this mechanics problem of resonat= ors =96<br> in case of the logarithmical frequency distribution, low near the apex to<b= r>high near the base =96 can be calculated, as I have done, analytically fo= r a<br>pure sinusoidal tone, which exactly results in a tonotopical symmetr= ical<br> envelope of that running phase wave with center frequency equal to the<br>c= orresponding resonance frequency.<br>And the running direction of that phas= e wave is always from base to apex.<br>Exactly as Tianying Ren has reported= in his then speech making paper that I<br> have cited:<br><br>Ren T. (2002) Longitudinal pattern of basilar membrane v= ibration in the<br>sensitive cochlea. Proc Nat Acad Sci USA 99: 17101-6.<br= ><br>The animation of such a phase wave can be seen in:<br><br><a href=3D"h= ttp://www.a3ccm-apmas-eakoh.be/aobmm/bm-movement.htm" target=3D"_blank">htt= p://www.a3ccm-apmas-eakoh.be/aobmm/bm-movement.htm</a><br> <br>You wrote:<br><br>**It sounds like you&#39;re trying to get away from a= Helmholtz-like conception<br> <div class=3D"im">of resonators or places responding to frequencies, and re= place it with a<br>more time-domain approach that works for a lot of pitch = phenomena. =A0But it<br></div>will work better to put that time-domain mech= anisms AFTER the what the<br> <div class=3D"im">cochlea does. =A0Each hair cell is a &quot;tap&quot; on t= he BM, reporting a time-domain<br>waveform as filtered by the traveling-wav= e mechanism; that&#39;s where the<br></div>pitch-processing nonlinear time-= domain operations start...**<br> <br>As you already have indicated in the beginning, you haven=92t studied t= he<br>booklet entirely. I know for sure that by not studying the booklet<br= >entirely, you have drawn premature conclusions here.<br><br>It is quite on= the contrary. I think that I have explained clearly enough<br> in the booklet that everywhere along the basilar membrane very local<br>res= onance with a high quality factor takes place. However not on the<br>primar= y sound pressure signal, but on the sound energy signal. Next to that<br> the basilar membrane will react everywhere =96 but not in a resonance mode<= br>and therefore with much smaller displacements =96 and will show a respon= se on<br>other frequency components, including utmost low frequencies even = until<br> stationary pressure signals.<br><br>And for the explanation of our hearing = sense I don=92t need a time domain<br>mechanism at all.<br>In the new parad= igm, described by me, from all the distinguishable<br>frequencies next of c= ourse to their frequency also their individual<br> amplitude and phase are transmitted to the auditory cortex.<br><br>Our brai= n can directly compare the entire frequency selected sound energy<br>stimul= us with patterns that are stored in our memory.<br><br>Actually I cannot im= agine a much more simpler and faster way.<br> <br>Finally about the definition of Ockham=92s Razor =96 also spelled Occam= =96 I<br>found on the Internet =A0the following physics educational websit= e:<br><br><a href=3D"http://math.ucr.edu/home/baez/physics/General/occam.ht= ml" target=3D"_blank">http://math.ucr.edu/home/baez/physics/General/occam.h= tml</a><br> <br>where among others a number of stronger but clear definitions are given= ,<br>and I cite:<br><br>*** If you have two theories that both explain the = observed facts, then you<br>should use the simplest until more evidence com= es along.<br> <br>The simplest explanation for some phenomenon is more likely to be accur= ate<br>than more complicated explanations.<br><br>If you have two equally l= ikely solutions to a problem, choose the simplest.<br><br>The explanation r= equiring the fewest assumptions is most likely to be<br> correct.<br><br>. . .or in the only form that takes its own advice. . .<br>= <br>Keep things simple! ***<br><br>Within this framework I am convinced tha= t I have done my utmost best.<br><br>So I am awaiting for a much better exp= lanation for the described beat<br> phenomena based on the current hearing paradigm.<br><br><br>Kind regards,<b= r><br>Pim Heerens<br></blockquote></div><br> --0016e65c8a628e7ed404ad70f091--


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