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: Thu, 22 Sep 2011 09:28:22 +0200 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY> --0016363b81cc35d7ee04ad82a3af Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable Hi Matt and list members, thanks for the support. One small comment to your statement that there are only forward traveling waves. I think much of the confusion stems from the fact that the observed motion of the cochlear partition is often referred t= o as the traveling wave. In actual fact this is only a 'reflection' of the actual wave which is traveling in the fluid. The fluid supports waves traveling in both directions, but the unique properties of the cochlea caus= e only the appearance of a forward traveling on the cochlear partition. If one wants to observe the reverse traveling waves in the cochlea it is necessary to measure fluid velocity, which I believe is not yet possible. Model calculations clearly show the reverse traveling wave and produce results in accordance with data on OAEs (see e.g. the work of Mauermann et al or Epp et al). But I'll (re)check the work of Ren to make sure I'm not relying only on what I believe to be true ;-). Thanks also to Charles for the support. And many thanks to Dick for startin= g the effort! All the best, Peter 2011/9/21 Matt Flax <flatmax@xxxxxxxx> > I am glad you brought this up again Peter, > > I have no problem with the passive travelling wave, however with respect > to actively induced movements, the latest experimental data shows that > there are ONLY forward travelling waves (check Ren's experiments for > example). > > OAEs are generated locally (this is common belief) consequently one > assumes that the basilar membrane is not on the surface, but suspended > inside the pond and the oval/round windows are on the surface of the > pond. > > What's more, if the OHCs in the apex are regarded as deep ocean > movements, then the waves resemble tsunamis ! Consequently only > movements near to the shore/surface (the windows) are easily observable > - the not easily observable being the small movements of the OHCs in the > apex themselves and the pressure waves (large in potential but tiny in > flux or velocity) in the incompressible fluid. > > Matt > > On Wed, 2011-09-21 at 12:21 +0200, Peter van Hengel wrote: > > Dear dr Heerens and list-members, > > > > I hesitate to get involved in this discussion as I have tried to > > explain the 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 force (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 we should attempt to integrate them with existing > > ones instead of throwing away 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 professor > > in applied physics, who reviewed our booklet during a > > contribution > > procedure for a scientific journal, quite recently gave us the > > verdict that > > 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 warned > > 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 messengers > > or designers of new paradigms are encountered by the mayor > > supporters of > > the competing one. Of course the scientific reputation > > rankings of so many > > 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 thread > > 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 wave > > 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 also > > acoustical vibration energy. How could an academic physics > > scientist reject > > 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 length > > always larger than 75 mm. > > So therefore this mechanism cannot contribute to a > > discriminating mechanism > > for frequency selectivity based on traveling waves. > > > > And regarding the "capillary" or "interfacial" waves I > > reject: yes indeed > > 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 resonance. > > > > ** > > > > 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: 149-213. > > > > 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 attache= d > > 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 classical > > waveguide resonance reflects a travelling wave, thus > > converting it into a > > standing wave devoid of the substantial phase-lag (ii); and > > produces a low- > > frequency cut-off instead of the high =96frequency cut-off (i). > > By contrast, another general type of travelling-wave system > > with resonance > > has become known more recently; initially, in a quite > > different context > > (physics of the atmosphere). This is described as > > critical-layer resonance, > > or else (because the reso=ACnance absorbs energy) > > critical-layer absorption. > > It yields a high-frequency cut-off; but, above all, it is > > characterized by > > the properties of the energy flow velocity. This falls to zero > > very steeply > > 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 light > > 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 observed > > 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 propagate > > 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 b= ase > > to near 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 now > > 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 the > > systematic mistuning of 1/16 =3D 0.0625 Hz. > > > > Additional changes in the mistuning, like for instance from > > 10004.0625 into > > 10003.9375 Hz, of either one, two or three of the mistuned > > frequencies are > > 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 of 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 10012 > > 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 als= o > > supported by > > Lighthill, will propagate by means of a traveling wave to one > > and the same > > 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 auditory > > cortex, where finally out of this =91Gordian knot of stimuli=92= a > > beep with 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 science, > > known as =91Ockham=92s Razor=92, to strive to an optimum in > > simplicity will be > > strongly violated. > > > > Your next remark: > > > > **You conclude that "the existence of two sound energy > > transport phenomena > > 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 for > > over 100 years to describe waves in fluids predicts exactly > > that behavior. > > Some may quibble that it has not been conclusively proved that > > the observed > > slow wave carries energy; but no workable alternative has been > > put forward, > > and no experiment convincingly contradicts this main > > hypothesis of the > > current paradigm, as far as I know. I know some on this list > > will probably > > > > say I'm wrong, now that I've opened the door.** > > > > Do you agree with me that the perilymph inside the cochlear > > duct, existing > > 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 the > > 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 basilar > > 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 on= ly > > place where > > 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 wave, > > 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 for 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 conception > > 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 it > > > > 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-domain > > 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 that > > the basilar membrane will react everywhere =96 but not in a > > resonance mode > > and therefore with much smaller displacements =96 and will show > > a response 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 spell= ed > > 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 you > > should use the simplest until more evidence comes along. > > > > The simplest explanation for some phenomenon is more likely to > > be accurate > > than more complicated explanations. > > > > If you have two equally likely solutions to a problem, choose > > the simplest. > > > > 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 > > > > > --0016363b81cc35d7ee04ad82a3af Content-Type: text/html; charset=windows-1252 Content-Transfer-Encoding: quoted-printable Hi Matt and list members, thanks for the support. One small comment = to your statement that there are only forward traveling waves. I think much= of the confusion stems from the fact that the observed motion of the cochl= ear partition is often referred to as the traveling wave. In actual fact th= is is only a 'reflection' of the actual wave which is traveling in = the fluid. The fluid supports waves traveling in both directions, but the u= nique properties of the cochlea cause only the appearance of a forward trav= eling on the cochlear partition. If one wants to observe the reverse traveling waves in the cochlea it is ne= cessary to measure fluid velocity, which I believe is not yet possible. Mod= el calculations clearly show the reverse traveling wave and produce results= in accordance with data on OAEs (see e.g. the work of Mauermann et al or E= pp et al). But I'll (re)check the work of Ren to make sure I'm not = relying only on what I believe to be true ;-). Thanks also to Charles for the support. And many thanks to Dick for startin= g the effort! All the best, Peter <div class=3D"gmail_quot= e">2011/9/21 Matt Flax <<a href=3D"mailto:flatmax@xxxxxxxx= .org">flatmax@xxxxxxxx</a>> <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p= x #ccc solid;padding-left:1ex;">I am glad you brought this up again Peter,<= br> I have no problem with the passive travelling wave, however with respect<br= > to actively induced movements, the latest experimental data shows that there are ONLY forward travelling waves (check Ren's experiments for<br= > example). OAEs are generated locally (this is common belief) consequently one assumes that the basilar membrane is not on the surface, but suspended inside the pond and the oval/round windows are on the surface of the pond. What's more, if the OHCs in the apex are regarded as deep ocean movements, then the waves resemble tsunamis ! Consequently only movements near to the shore/surface (the windows) are easily observable - the not easily observable being the small movements of the OHCs in the<br= > apex themselves and the pressure waves (large in potential but tiny in flux or velocity) in the incompressible fluid. Matt <div><div></div><div class=3D"h5"> On Wed, 2011-09-21 at 12:21 +0200, Peter van Hengel wrote: > Dear dr Heerens and list-members, > > I hesitate to get involved in this discussion as I have tried to > explain the hydrodynamics behind (transmission line) cochlea models<br= > > before in another thread on this list and don't like repeating mys= elf. > But I feel I have to lend my support the comments made by Dick Lyon.<b= r> > 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)<b= r> > MUST exhibit 'ripples' on the surface. In the cochlea these ar= e > 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 unfortu= nately > 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<= br> > modeling physiological, pshychophysical and OAE date, I'll stick w= ith > the transmission line. Things like pitch perception and the missing<br= > > 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<br= > > new theories, but we should attempt to integrate them with existing<br= > > ones instead of throwing away something that has proven to work. > > Kind regards, > Peter van Hengel > > </div></div><div class=3D"im">> 2011/9/19 Willem Christiaan Heerens <= <a href=3D"mailto:heerens1@xxxxxxxx">heerens1@xxxxxxxx</a>> </div><div><div></div><div class=3D"h5">> =A0 =A0 =A0 =A0 Dear Dick Lyon= , > > > =A0 =A0 =A0 =A0 Thank you for your substantial list of comments. =A0Of= course I > =A0 =A0 =A0 =A0 will reply. > =A0 =A0 =A0 =A0 With pleasure. > > =A0 =A0 =A0 =A0 You wrote: > =A0 =A0 =A0 =A0 **Sometimes it's hard to get a reaction when you a= re trying to > =A0 =A0 =A0 =A0 replace a > =A0 =A0 =A0 =A0 paradigm, as the silence here illustrates. =A0I didn&#= 39;t really > =A0 =A0 =A0 =A0 get into the > =A0 =A0 =A0 =A0 new ideas of your book much, but I have some comments = on the > =A0 =A0 =A0 =A0 introductory > > =A0 =A0 =A0 =A0 material about why you reject the current paradigm.**<= br> > > =A0 =A0 =A0 =A0 Your reaction in the first sentence is pretty well fam= iliar to > =A0 =A0 =A0 =A0 me. It is > =A0 =A0 =A0 =A0 entirely in accordance with the procedure described by= Thomas > =A0 =A0 =A0 =A0 Kuhn in his > =A0 =A0 =A0 =A0 world famous 1962 =A0essay: > > =A0 =A0 =A0 =A0 =93The Structure of Scientific Revolutions=94 > > =A0 =A0 =A0 =A0 Besides that: a former colleague of mine, a highly ski= lled > =A0 =A0 =A0 =A0 senior professor > =A0 =A0 =A0 =A0 in applied physics, who reviewed our booklet during a<= br> > =A0 =A0 =A0 =A0 contribution > =A0 =A0 =A0 =A0 procedure for a scientific journal, quite recently gav= e us the > =A0 =A0 =A0 =A0 verdict that > =A0 =A0 =A0 =A0 he fully agreed with our arguments and statements and = he urged > =A0 =A0 =A0 =A0 the editor > =A0 =A0 =A0 =A0 to make a full scientific discussion possible for our = views. > =A0 =A0 =A0 =A0 He also warned > =A0 =A0 =A0 =A0 me that to be in right is not the same as to be put in= right. > =A0 =A0 =A0 =A0 I myself > =A0 =A0 =A0 =A0 don=92t see all this as a problematic issue. It=92s pa= rt of the > =A0 =A0 =A0 =A0 way messengers > =A0 =A0 =A0 =A0 or designers of new paradigms are encountered by the m= ayor > =A0 =A0 =A0 =A0 supporters of > =A0 =A0 =A0 =A0 the competing one. Of course the scientific reputation= > =A0 =A0 =A0 =A0 rankings of so many > =A0 =A0 =A0 =A0 scientists are involved and in danger in case a paradi= gm shift > =A0 =A0 =A0 =A0 is > =A0 =A0 =A0 =A0 happening. > > =A0 =A0 =A0 =A0 The only issue that counts for me is that scientific a= rguments > =A0 =A0 =A0 =A0 from both > =A0 =A0 =A0 =A0 sides brought in discussion, verified and weighted in = a > =A0 =A0 =A0 =A0 careful way must > =A0 =A0 =A0 =A0 turn the balance. Ignoring irrefutable arguments becau= se they > =A0 =A0 =A0 =A0 form a thread > =A0 =A0 =A0 =A0 for the ranking of a scientist has always been contra<= br> > =A0 =A0 =A0 =A0 productive for the > =A0 =A0 =A0 =A0 progress in a field of science. History shows many of = such > =A0 =A0 =A0 =A0 examples. One of > =A0 =A0 =A0 =A0 the most salient among them certainly is the Copernica= n > =A0 =A0 =A0 =A0 revolution. > > =A0 =A0 =A0 =A0 The result of the second line of your comment I really= regret, > =A0 =A0 =A0 =A0 because in > =A0 =A0 =A0 =A0 the rest of your writings I clearly can see that you h= ave > =A0 =A0 =A0 =A0 apparently > =A0 =A0 =A0 =A0 missed, misread or misinterpreted a number of issues o= n > =A0 =A0 =A0 =A0 cardinal points. > > =A0 =A0 =A0 =A0 Let me discuss your next comment: > > =A0 =A0 =A0 =A0 **You discuss and reject two wave concepts: first, the= > =A0 =A0 =A0 =A0 pressure sound wave > =A0 =A0 =A0 =A0 that travels so fast that wavelengths will always be l= ong > =A0 =A0 =A0 =A0 compared to the > =A0 =A0 =A0 =A0 size of the cochlea, and second, "capillary"= or "interfacial" > =A0 =A0 =A0 =A0 waves, > =A0 =A0 =A0 =A0 presumably meaning those water surface waves where gra= vity > =A0 =A0 =A0 =A0 provides the > =A0 =A0 =A0 =A0 restoring force. =A0Of course, neither of these can be= the > =A0 =A0 =A0 =A0 explanation for > > =A0 =A0 =A0 =A0 how the cochlea works.** > > =A0 =A0 =A0 =A0 I don=92t reject the pressure sound wave concept, at l= east not > =A0 =A0 =A0 =A0 in general. It > =A0 =A0 =A0 =A0 is of course the vehicle of mechanical vibration energ= y and > =A0 =A0 =A0 =A0 therefore also > =A0 =A0 =A0 =A0 acoustical vibration energy. How could an academic phy= sics > =A0 =A0 =A0 =A0 scientist reject > =A0 =A0 =A0 =A0 that? > =A0 =A0 =A0 =A0 What I have argued is that for all the frequencies tha= t can be > =A0 =A0 =A0 =A0 sensed in > =A0 =A0 =A0 =A0 the cochlea even up to 20 kHz counts that the sound ve= locity > =A0 =A0 =A0 =A0 in perilymph =96 > =A0 =A0 =A0 =A0 being 1500 m/s =96 in relation with these frequencies = result in > =A0 =A0 =A0 =A0 a wave length > =A0 =A0 =A0 =A0 always larger than 75 mm. > =A0 =A0 =A0 =A0 So therefore this mechanism cannot contribute to a > =A0 =A0 =A0 =A0 discriminating mechanism > =A0 =A0 =A0 =A0 for frequency selectivity based on traveling waves.<br= > > > =A0 =A0 =A0 =A0 And regarding the =A0"capillary" or "in= terfacial" waves I > =A0 =A0 =A0 =A0 reject: yes indeed > =A0 =A0 =A0 =A0 in quite a number of textbooks I see the comparison of= the > =A0 =A0 =A0 =A0 propagation of > =A0 =A0 =A0 =A0 surface waves in a pond with the slow waves inside the= > =A0 =A0 =A0 =A0 cochlea. It simply > =A0 =A0 =A0 =A0 is an erroneous analogon. None of the parameters neces= sary for > =A0 =A0 =A0 =A0 the > =A0 =A0 =A0 =A0 existence of capillary waves can be found inside the c= ochlea. > =A0 =A0 =A0 =A0 So neither > =A0 =A0 =A0 =A0 they can play a role in evoking traveling waves that h= ave > =A0 =A0 =A0 =A0 short wavelengths. > > =A0 =A0 =A0 =A0 You wrote: > > =A0 =A0 =A0 =A0 **You also attribute to Lighthill some strange wrong i= deas > =A0 =A0 =A0 =A0 about > =A0 =A0 =A0 =A0 transmission lines only being able to transmit energy = near > =A0 =A0 =A0 =A0 their resonance. > > =A0 =A0 =A0 =A0 ** > > =A0 =A0 =A0 =A0 Can you be more specific? =A0The only lines I describe= are the > =A0 =A0 =A0 =A0 lines in Fig. > =A0 =A0 =A0 =A0 1. That figure is a reproduction of the figure in Ligh= thill=92s > =A0 =A0 =A0 =A0 paper: > > =A0 =A0 =A0 =A0 Lighthill MJ. (1981) Energy flow in the cochlea. J Flu= id Mech > =A0 =A0 =A0 =A0 106: 149-213. > > =A0 =A0 =A0 =A0 I haven=92t attributed strange wrong ideas to Lighthil= l. I have > =A0 =A0 =A0 =A0 studied > =A0 =A0 =A0 =A0 carefully all the 64 pages =A0of his paper. > > =A0 =A0 =A0 =A0 He starts with a very informative series of premises a= nd I > =A0 =A0 =A0 =A0 cite this part: > > =A0 =A0 =A0 =A0 *** With moderate acoustic stimuli, measurements of<br= > > =A0 =A0 =A0 =A0 basilar-membrane > =A0 =A0 =A0 =A0 vibration (especially, those using a M=F6ssbauer sourc= e attached > =A0 =A0 =A0 =A0 to the > =A0 =A0 =A0 =A0 membrane) demonstrate: > =A0 =A0 =A0 =A0 (i) a high degree of asymmetry, in that the response t= o a pure > =A0 =A0 =A0 =A0 tone falls > =A0 =A0 =A0 =A0 extremely sharply above the characteristic frequency, = although > =A0 =A0 =A0 =A0 much more > =A0 =A0 =A0 =A0 gradually below it; > =A0 =A0 =A0 =A0 (ii) a substantial phase-lag in that response, and one= which > =A0 =A0 =A0 =A0 increases > =A0 =A0 =A0 =A0 monotonically tip to the characteristic frequency; > =A0 =A0 =A0 =A0 (iii) a response to a 'click' in the form of a= delayed > =A0 =A0 =A0 =A0 'ringing' > =A0 =A0 =A0 =A0 oscillation at the characteristic frequency, which per= sists > =A0 =A0 =A0 =A0 for around 20 > =A0 =A0 =A0 =A0 cycles. > =A0 =A0 =A0 =A0 This paper uses energy-flow considerations to identify= which > =A0 =A0 =A0 =A0 features in a > =A0 =A0 =A0 =A0 mathe=ACmatical model of cochlear mechanics are necess= ary if it > =A0 =A0 =A0 =A0 is to > =A0 =A0 =A0 =A0 reproduce these experi=ACmental findings. > =A0 =A0 =A0 =A0 The response (iii) demands a travelling-wave model whi= ch > =A0 =A0 =A0 =A0 incorporates an > =A0 =A0 =A0 =A0 only lightly damped resonance. Admittedly, waveguide s= ystems > =A0 =A0 =A0 =A0 including > =A0 =A0 =A0 =A0 resonance are described in classical applied physics. = However, > =A0 =A0 =A0 =A0 a classical > =A0 =A0 =A0 =A0 waveguide resonance reflects a travelling wave, thus<b= r> > =A0 =A0 =A0 =A0 converting it into a > =A0 =A0 =A0 =A0 standing wave devoid of the substantial phase-lag (ii)= ; and > =A0 =A0 =A0 =A0 produces a low- > =A0 =A0 =A0 =A0 frequency cut-off instead of the high =96frequency cut= -off (i). > =A0 =A0 =A0 =A0 By contrast, another general type of travelling-wave s= ystem > =A0 =A0 =A0 =A0 with resonance > =A0 =A0 =A0 =A0 has become known more recently; initially, in a quite<= br> > =A0 =A0 =A0 =A0 different context > =A0 =A0 =A0 =A0 (physics of the atmosphere). This is described as > =A0 =A0 =A0 =A0 critical-layer resonance, > =A0 =A0 =A0 =A0 or else (because the reso=ACnance =A0absorbs energy)<b= r> > =A0 =A0 =A0 =A0 critical-layer absorption. > =A0 =A0 =A0 =A0 It yields a high-frequency cut-off; but, above all, it= is > =A0 =A0 =A0 =A0 characterized by > =A0 =A0 =A0 =A0 the properties of the energy flow velocity. This falls= to zero > =A0 =A0 =A0 =A0 very steeply > =A0 =A0 =A0 =A0 as the point of resonance is approached; so that wave = energy > =A0 =A0 =A0 =A0 flow is > =A0 =A0 =A0 =A0 retarded drastically, giving any light damping which i= s > =A0 =A0 =A0 =A0 present an > =A0 =A0 =A0 =A0 unlimited time in which to dissipate that energy. > =A0 =A0 =A0 =A0 Existing mathematical models of cochlear mechanics, wh= ether > =A0 =A0 =A0 =A0 using one-, two- > =A0 =A0 =A0 =A0 =A0or three-dimensional representations of cochlear ge= ometry, > =A0 =A0 =A0 =A0 are analysed > =A0 =A0 =A0 =A0 from this standpoint. All are found to have been succe= ssful > =A0 =A0 =A0 =A0 (if only light > =A0 =A0 =A0 =A0 damping is incorporated, as (iii) requires) when and o= nly when > =A0 =A0 =A0 =A0 they > =A0 =A0 =A0 =A0 incorporate critical-layer absorption. This resolves t= he > =A0 =A0 =A0 =A0 paradox of why > =A0 =A0 =A0 =A0 certain grossly unrealistic one-dimensional models can= give a > =A0 =A0 =A0 =A0 good > =A0 =A0 =A0 =A0 prediction of cochlear response; it is because they<br= > > =A0 =A0 =A0 =A0 incorporate the one > =A0 =A0 =A0 =A0 dimensional feature of critical-layer absorption.***<b= r> > > =A0 =A0 =A0 =A0 Apparently Lighthill has never considered the possibil= ity that > =A0 =A0 =A0 =A0 the observed > =A0 =A0 =A0 =A0 movements of the basilar membrane could be caused by a= nother > =A0 =A0 =A0 =A0 phenomenon > =A0 =A0 =A0 =A0 than a sound energy transporting traveling wave. > > =A0 =A0 =A0 =A0 Your next remark: > > =A0 =A0 =A0 =A0 **Actually, he showed the opposite: =A0that a sinusoid= al wave > =A0 =A0 =A0 =A0 will propagate > =A0 =A0 =A0 =A0 until the point where the transmission line resonance = gets low > =A0 =A0 =A0 =A0 enough to > =A0 =A0 =A0 =A0 match the wave frequency, and at that point it will sl= ow down > =A0 =A0 =A0 =A0 to zero > =A0 =A0 =A0 =A0 velocity and die out. =A0This is not exactly how the c= ochlea > =A0 =A0 =A0 =A0 works (the BM is > =A0 =A0 =A0 =A0 not very resonant), but not a bad concept from base to= near > =A0 =A0 =A0 =A0 the best > =A0 =A0 =A0 =A0 place.** > > > =A0 =A0 =A0 =A0 You say it clearly enough: =A0 =91It isn=92t a bad con= cept from base > =A0 =A0 =A0 =A0 to near the > =A0 =A0 =A0 =A0 best place.=92 > =A0 =A0 =A0 =A0 So not having an exact agreement between theory and pr= actice > =A0 =A0 =A0 =A0 makes the > =A0 =A0 =A0 =A0 underlying hypothesis directly vulnerable for falsific= ation. > > =A0 =A0 =A0 =A0 Indeed the cochlea cannot react like that. And I want = to make > =A0 =A0 =A0 =A0 this clear by > =A0 =A0 =A0 =A0 the following series of experiments: > > =A0 =A0 =A0 =A0 Entirely based on the premises of the new paradigm I h= ave > =A0 =A0 =A0 =A0 described, I now > =A0 =A0 =A0 =A0 have calculated a number of predictable sound phenomen= a by > =A0 =A0 =A0 =A0 using the > =A0 =A0 =A0 =A0 following frequencies together with prescribed phase r= elations > =A0 =A0 =A0 =A0 in a > =A0 =A0 =A0 =A0 standard summation procedure to compose a Fourier seri= es: > > =A0 =A0 =A0 =A0 1: > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A010000 + 10004 + 10008 + 10012 += 10016 + 10020 + > =A0 =A0 =A0 =A0 10024 Hz > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 Where all the contributions ar= e sine functions. > > =A0 =A0 =A0 =A0 Our paradigm predicts: =A0an undisputable beat of 4 Hz= in a high > =A0 =A0 =A0 =A0 beep tone. > > =A0 =A0 =A0 =A0 2: > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A010000 + 10004 + 10008 + 10012 += 10016 + 10020 + > =A0 =A0 =A0 =A0 10024 Hz > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Where the contributions are suc= cessively > =A0 =A0 =A0 =A0 alternating sine and > =A0 =A0 =A0 =A0 cosine functions. > > =A0 =A0 =A0 =A0 Our paradigm now predicts: =A0an undisputable beat of = 8 Hz in > =A0 =A0 =A0 =A0 the same high > =A0 =A0 =A0 =A0 beep tone. > > =A0 =A0 =A0 =A0 3: > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A010000 + 10004.0625 + 10008 + 10= 012.0625 + 10016 + > =A0 =A0 =A0 =A0 10020.0625 + > =A0 =A0 =A0 =A0 10024 Hz > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Where all the contributions are= sine functions. > > =A0 =A0 =A0 =A0 Our paradigm now predicts: =A0a =A0beep, in which an u= ndisputable > =A0 =A0 =A0 =A0 beat exists > =A0 =A0 =A0 =A0 that changes every 8 seconds from clearly 4 Hz to 8 Hz= and > =A0 =A0 =A0 =A0 then reverses > =A0 =A0 =A0 =A0 again to 4 Hz. So the beat pattern has a period of 8 s= econds > =A0 =A0 =A0 =A0 caused by the > =A0 =A0 =A0 =A0 systematic mistuning of 1/16 =3D 0.0625 Hz. > > =A0 =A0 =A0 =A0 Additional changes in the mistuning, like for instance= from > =A0 =A0 =A0 =A0 10004.0625 into > =A0 =A0 =A0 =A0 10003.9375 Hz, of either one, two or three of the mist= uned > =A0 =A0 =A0 =A0 frequencies are > =A0 =A0 =A0 =A0 predicted to give the same results in the beat pattern= as > =A0 =A0 =A0 =A0 experiment 3. > > =A0 =A0 =A0 =A0 And actually I want to urge everybody to download the = software > =A0 =A0 =A0 =A0 program of > =A0 =A0 =A0 =A0 Yves Mangelinckx =A0with which these sound complexes c= an be > =A0 =A0 =A0 =A0 properly > =A0 =A0 =A0 =A0 calculated in the form of wav files from the following= site: > > =A0 =A0 =A0 =A0 <a href=3D"http://www.a3ccm-apmas-eakoh.be/a3ccm-apmas= -eakoh-index.htm" target=3D"_blank">http://www.a3ccm-apmas-eakoh.be/a3ccm-a= pmas-eakoh-index.htm</a> > > =A0 =A0 =A0 =A0 [ NOTE: =A0 =A0The standard setting in the 1/f mode in= this > =A0 =A0 =A0 =A0 software program > =A0 =A0 =A0 =A0 takes care that all the individually primary calculate= d > =A0 =A0 =A0 =A0 frequencies > =A0 =A0 =A0 =A0 contribute equal energy to the resulting sound pressur= e > =A0 =A0 =A0 =A0 signal. This > =A0 =A0 =A0 =A0 condition is very important for the influences on pitc= h > =A0 =A0 =A0 =A0 calculations in > =A0 =A0 =A0 =A0 case higher values of the differences between contribu= ting > =A0 =A0 =A0 =A0 frequencies > =A0 =A0 =A0 =A0 exist. ] > > =A0 =A0 =A0 =A0 This in order to give the interested reader the opport= unity to > =A0 =A0 =A0 =A0 falsify or =96 > =A0 =A0 =A0 =A0 in case our predictions are correct =96 to verify our = findings. > > =A0 =A0 =A0 =A0 And of course I wouldn=92t have given these examples i= f I wasn=92t > =A0 =A0 =A0 =A0 sure of my > =A0 =A0 =A0 =A0 statements. > =A0 =A0 =A0 =A0 I can already inform you that verification will be the= result. > > =A0 =A0 =A0 =A0 If you carry out the same series of experiments with a= start > =A0 =A0 =A0 =A0 frequency of > =A0 =A0 =A0 =A0 1000 Hz instead of 10000 Hz, you will hear the same se= ries of > =A0 =A0 =A0 =A0 beat > =A0 =A0 =A0 =A0 phenomena, but now with the lower beep of the 1012 Hz = instead > =A0 =A0 =A0 =A0 of the 10012 > =A0 =A0 =A0 =A0 Hz beep. > =A0 =A0 =A0 =A0 Even if you go down with the start frequency to 200 Hz= or 400 > =A0 =A0 =A0 =A0 Hz you will > =A0 =A0 =A0 =A0 still hear the same beat phenomena, but now with the l= ow > =A0 =A0 =A0 =A0 humming tone of > =A0 =A0 =A0 =A0 200 Hz respectively with the one octave higher humming= tone of > =A0 =A0 =A0 =A0 400 Hz. > > =A0 =A0 =A0 =A0 Hence it is a perception phenomenon that appears all o= ver the > =A0 =A0 =A0 =A0 entire > =A0 =A0 =A0 =A0 auditory frequency range. > > =A0 =A0 =A0 =A0 And it must be remarked that according to the current = hearing > =A0 =A0 =A0 =A0 theory all > =A0 =A0 =A0 =A0 the used frequencies =96 especially in the higher freq= uencies > =A0 =A0 =A0 =A0 like in the > =A0 =A0 =A0 =A0 10000 Hz experiments =96 according to auditory experts= , and also > =A0 =A0 =A0 =A0 supported by > =A0 =A0 =A0 =A0 Lighthill, will propagate by means of a traveling wave= to one > =A0 =A0 =A0 =A0 and the same > =A0 =A0 =A0 =A0 location on the basilar membrane. > > =A0 =A0 =A0 =A0 If we then still follow the current hearing paradigm, = we have > =A0 =A0 =A0 =A0 to believe > =A0 =A0 =A0 =A0 that the medley of that seven totally unresolved frequ= encies > =A0 =A0 =A0 =A0 will be > =A0 =A0 =A0 =A0 transferred via one and the same nerve fiber to a loca= tion in > =A0 =A0 =A0 =A0 the auditory > =A0 =A0 =A0 =A0 cortex, where finally out of this =91Gordian knot of s= timuli=92 a > =A0 =A0 =A0 =A0 beep with the > =A0 =A0 =A0 =A0 described and also heard beat patterns will be reconst= ructed. > > =A0 =A0 =A0 =A0 Once these beat phenomena are verified as really exist= ing for > =A0 =A0 =A0 =A0 every > =A0 =A0 =A0 =A0 listener with a reasonable normal hearing, do you agre= e with > =A0 =A0 =A0 =A0 me that for > =A0 =A0 =A0 =A0 the current paradigm this is a very serious anomaly?<b= r> > =A0 =A0 =A0 =A0 In my opinion forcing an explanation within the framew= ork of > =A0 =A0 =A0 =A0 the current > =A0 =A0 =A0 =A0 paradigm will result in such a complexity that the gen= eral > =A0 =A0 =A0 =A0 rule in science, > =A0 =A0 =A0 =A0 known as =A0=91Ockham=92s Razor=92, to strive to an op= timum in > =A0 =A0 =A0 =A0 simplicity will be > =A0 =A0 =A0 =A0 strongly violated. > > =A0 =A0 =A0 =A0 Your next remark: > > =A0 =A0 =A0 =A0 **You conclude that "the existence of two sound e= nergy > =A0 =A0 =A0 =A0 transport phenomena > =A0 =A0 =A0 =A0 with different transfer velocities within this tiny co= chlear > =A0 =A0 =A0 =A0 volume of > =A0 =A0 =A0 =A0 perilymph fluid as suggested by Lighthill is impossibl= e." =A0Yet > =A0 =A0 =A0 =A0 all > =A0 =A0 =A0 =A0 observations do see a slow wave, much slower than the = speed of > =A0 =A0 =A0 =A0 sound, and > =A0 =A0 =A0 =A0 basic mathematical physics of the same sort that has b= een > =A0 =A0 =A0 =A0 working well for > =A0 =A0 =A0 =A0 over 100 years to describe waves in fluids predicts ex= actly > =A0 =A0 =A0 =A0 that behavior. > =A0 =A0 =A0 =A0 Some may quibble that it has not been conclusively pro= ved that > =A0 =A0 =A0 =A0 the observed > =A0 =A0 =A0 =A0 slow wave carries energy; but no workable alternative = has been > =A0 =A0 =A0 =A0 put forward, > =A0 =A0 =A0 =A0 and no experiment convincingly contradicts this main<b= r> > =A0 =A0 =A0 =A0 hypothesis of the > =A0 =A0 =A0 =A0 current paradigm, as far as I know. =A0I know some on = this list > =A0 =A0 =A0 =A0 will probably > > =A0 =A0 =A0 =A0 say I'm wrong, now that I've opened the door.*= * > > =A0 =A0 =A0 =A0 Do you agree with me that the perilymph inside the coc= hlear > =A0 =A0 =A0 =A0 duct, existing > =A0 =A0 =A0 =A0 of scala vestibuli and scala tympani, is just moving b= ack and > =A0 =A0 =A0 =A0 forth over > =A0 =A0 =A0 =A0 distances not exceeding a few micrometer? > > =A0 =A0 =A0 =A0 If you admit this fact, you should also agree with me = that all > =A0 =A0 =A0 =A0 the known > =A0 =A0 =A0 =A0 and involved physical quantities and parameters indica= te that > =A0 =A0 =A0 =A0 we are > =A0 =A0 =A0 =A0 confronted here with the problem to find the hydrodyna= mic > =A0 =A0 =A0 =A0 solution for the > =A0 =A0 =A0 =A0 non-stationary small movements of an incompressible<br= > > =A0 =A0 =A0 =A0 non-viscous fluid in a > =A0 =A0 =A0 =A0 tiny narrow duct. > =A0 =A0 =A0 =A0 According to the rules of physics it is then permitted= without > =A0 =A0 =A0 =A0 any > =A0 =A0 =A0 =A0 additional constraints to use the non-stationary Berno= ulli > =A0 =A0 =A0 =A0 equation. > > =A0 =A0 =A0 =A0 The exact and detailed solution of this equation I can= =96 if > =A0 =A0 =A0 =A0 you wish =96 send > =A0 =A0 =A0 =A0 you separately. > > =A0 =A0 =A0 =A0 The result is exactly the mathematical expression I ha= ve used > =A0 =A0 =A0 =A0 in the > =A0 =A0 =A0 =A0 booklet: =A0the pressure decrease in the perilymph duc= t in front > =A0 =A0 =A0 =A0 of the > =A0 =A0 =A0 =A0 basilar membrane is everywhere proportional to the per= ilymph > =A0 =A0 =A0 =A0 velocity > =A0 =A0 =A0 =A0 squared. > =A0 =A0 =A0 =A0 What leads to the overall result that the pressure sti= mulus on > =A0 =A0 =A0 =A0 the basilar > =A0 =A0 =A0 =A0 membrane is proportional to the sound energy stimulus = offered > =A0 =A0 =A0 =A0 to the ear. > > =A0 =A0 =A0 =A0 You further wrote: > > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 **Yet all observations do see a sl= ow wave, much > =A0 =A0 =A0 =A0 slower than the > =A0 =A0 =A0 =A0 speed of sound.** > > =A0 =A0 =A0 =A0 Indeed, an observation of a =91slow wavy movement=92 a= nd the only > =A0 =A0 =A0 =A0 place where > =A0 =A0 =A0 =A0 we can observe this is the basilar membrane. > > =A0 =A0 =A0 =A0 It isn=92t the occurrence of a wavy movement phenomeno= n that we > =A0 =A0 =A0 =A0 have to > =A0 =A0 =A0 =A0 discuss. It is the origin of that =91traveling wave=92= that we > =A0 =A0 =A0 =A0 have to > =A0 =A0 =A0 =A0 discover. Is it a vibration energy transporting wave o= r is it > =A0 =A0 =A0 =A0 a phase wave, > =A0 =A0 =A0 =A0 originated out of the manner in which the resonators i= n the > =A0 =A0 =A0 =A0 basilar > =A0 =A0 =A0 =A0 membrane are grouped? > > =A0 =A0 =A0 =A0 By the way, that is also =96 but not in an extended wa= y =96 > =A0 =A0 =A0 =A0 explained in our > =A0 =A0 =A0 =A0 booklet. In that chapter of the booklet I describe why= those > =A0 =A0 =A0 =A0 =91waves=92 always > =A0 =A0 =A0 =A0 run from base to apex. It is conform to the peculiar m= echanics > =A0 =A0 =A0 =A0 of the > =A0 =A0 =A0 =A0 basilar membrane system that this phase wave behavior = is > =A0 =A0 =A0 =A0 prescribed as it > =A0 =A0 =A0 =A0 is. > =A0 =A0 =A0 =A0 And that mathematical solution for this mechanics prob= lem of > =A0 =A0 =A0 =A0 resonators =96 > =A0 =A0 =A0 =A0 in case of the logarithmical frequency distribution, l= ow near > =A0 =A0 =A0 =A0 the apex to > =A0 =A0 =A0 =A0 high near the base =96 can be calculated, as I have do= ne, > =A0 =A0 =A0 =A0 analytically for a > =A0 =A0 =A0 =A0 pure sinusoidal tone, which exactly results in a tonot= opical > =A0 =A0 =A0 =A0 symmetrical > =A0 =A0 =A0 =A0 envelope of that running phase wave with center freque= ncy > =A0 =A0 =A0 =A0 equal to the > =A0 =A0 =A0 =A0 corresponding resonance frequency. > =A0 =A0 =A0 =A0 And the running direction of that phase wave is always= from > =A0 =A0 =A0 =A0 base to apex. > =A0 =A0 =A0 =A0 Exactly as Tianying Ren has reported in his then speec= h making > =A0 =A0 =A0 =A0 paper that I > =A0 =A0 =A0 =A0 have cited: > > =A0 =A0 =A0 =A0 Ren T. (2002) Longitudinal pattern of basilar membrane= > =A0 =A0 =A0 =A0 vibration in the > =A0 =A0 =A0 =A0 sensitive cochlea. Proc Nat Acad Sci USA 99: 17101-6.<= br> > > =A0 =A0 =A0 =A0 The animation of such a phase wave can be seen in: > > =A0 =A0 =A0 =A0 <a href=3D"http://www.a3ccm-apmas-eakoh.be/aobmm/bm-mo= vement.htm" target=3D"_blank">http://www.a3ccm-apmas-eakoh.be/aobmm/bm-move= ment.htm</a> > > =A0 =A0 =A0 =A0 You wrote: > > =A0 =A0 =A0 =A0 **It sounds like you're trying to get away from a<= br> > =A0 =A0 =A0 =A0 Helmholtz-like conception > =A0 =A0 =A0 =A0 of resonators or places responding to frequencies, and= replace > =A0 =A0 =A0 =A0 it with a > =A0 =A0 =A0 =A0 more time-domain approach that works for a lot of pitc= h > =A0 =A0 =A0 =A0 phenomena. =A0But it > > =A0 =A0 =A0 =A0 will work better to put that time-domain mechanisms AF= TER the > =A0 =A0 =A0 =A0 what the > =A0 =A0 =A0 =A0 cochlea does. =A0Each hair cell is a "tap" o= n the BM, reporting > =A0 =A0 =A0 =A0 a time-domain > =A0 =A0 =A0 =A0 waveform as filtered by the traveling-wave mechanism; = that's > =A0 =A0 =A0 =A0 where the > > =A0 =A0 =A0 =A0 pitch-processing nonlinear time-domain operations star= t...** > > =A0 =A0 =A0 =A0 As you already have indicated in the beginning, you ha= ven=92t > =A0 =A0 =A0 =A0 studied the > =A0 =A0 =A0 =A0 booklet entirely. I know for sure that by not studying= the > =A0 =A0 =A0 =A0 booklet > =A0 =A0 =A0 =A0 entirely, you have drawn premature conclusions here.<b= r> > > =A0 =A0 =A0 =A0 It is quite on the contrary. I think that I have expla= ined > =A0 =A0 =A0 =A0 clearly enough > =A0 =A0 =A0 =A0 in the booklet that everywhere along the basilar membr= ane very > =A0 =A0 =A0 =A0 local > =A0 =A0 =A0 =A0 resonance with a high quality factor takes place. Howe= ver not > =A0 =A0 =A0 =A0 on the > =A0 =A0 =A0 =A0 primary sound pressure signal, but on the sound energy= signal. > =A0 =A0 =A0 =A0 Next to that > =A0 =A0 =A0 =A0 the basilar membrane will react everywhere =96 but not= in a > =A0 =A0 =A0 =A0 resonance mode > =A0 =A0 =A0 =A0 and therefore with much smaller displacements =96 and = will show > =A0 =A0 =A0 =A0 a response on > =A0 =A0 =A0 =A0 other frequency components, including utmost low frequ= encies > =A0 =A0 =A0 =A0 even until > =A0 =A0 =A0 =A0 stationary pressure signals. > > =A0 =A0 =A0 =A0 And for the explanation of our hearing sense I don=92t= need a > =A0 =A0 =A0 =A0 time domain > =A0 =A0 =A0 =A0 mechanism at all. > =A0 =A0 =A0 =A0 In the new paradigm, described by me, from all the > =A0 =A0 =A0 =A0 distinguishable > =A0 =A0 =A0 =A0 frequencies next of course to their frequency also the= ir > =A0 =A0 =A0 =A0 individual > =A0 =A0 =A0 =A0 amplitude and phase are transmitted to the auditory co= rtex. > > =A0 =A0 =A0 =A0 Our brain can directly compare the entire frequency se= lected > =A0 =A0 =A0 =A0 sound energy > =A0 =A0 =A0 =A0 stimulus with patterns that are stored in our memory.<= br> > > =A0 =A0 =A0 =A0 Actually I cannot imagine a much more simpler and fast= er way. > > =A0 =A0 =A0 =A0 Finally about the definition of Ockham=92s Razor =96 a= lso spelled > =A0 =A0 =A0 =A0 Occam =96 I > =A0 =A0 =A0 =A0 found on the Internet =A0the following physics educati= onal > =A0 =A0 =A0 =A0 website: > > =A0 =A0 =A0 =A0 <a href=3D"http://math.ucr.edu/home/baez/physics/Gener= al/occam.html" target=3D"_blank">http://math.ucr.edu/home/baez/physics/Gene= ral/occam.html</a> > > =A0 =A0 =A0 =A0 where among others a number of stronger but clear defi= nitions > =A0 =A0 =A0 =A0 are given, > =A0 =A0 =A0 =A0 and I cite: > > =A0 =A0 =A0 =A0 *** If you have two theories that both explain the obs= erved > =A0 =A0 =A0 =A0 facts, then you > =A0 =A0 =A0 =A0 should use the simplest until more evidence comes alon= g. > > =A0 =A0 =A0 =A0 The simplest explanation for some phenomenon is more l= ikely to > =A0 =A0 =A0 =A0 be accurate > =A0 =A0 =A0 =A0 than more complicated explanations. > > =A0 =A0 =A0 =A0 If you have two equally likely solutions to a problem,= choose > =A0 =A0 =A0 =A0 the simplest. > > =A0 =A0 =A0 =A0 The explanation requiring the fewest assumptions is mo= st > =A0 =A0 =A0 =A0 likely to be > =A0 =A0 =A0 =A0 correct. > > =A0 =A0 =A0 =A0 . . .or in the only form that takes its own advice. . = . > > =A0 =A0 =A0 =A0 Keep things simple! *** > > =A0 =A0 =A0 =A0 Within this framework I am convinced that I have done = my > =A0 =A0 =A0 =A0 utmost best. > > =A0 =A0 =A0 =A0 So I am awaiting for a much better explanation for the= > =A0 =A0 =A0 =A0 described beat > =A0 =A0 =A0 =A0 phenomena based on the current hearing paradigm. > > > =A0 =A0 =A0 =A0 Kind regards, > > =A0 =A0 =A0 =A0 Pim Heerens > </div></div></blockquote></div> --0016363b81cc35d7ee04ad82a3af--

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Electrical Engineering Dept., Columbia University