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 11:16:47 +0200
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

--0016363b81cc02b65604ad842719 Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable Hi Matt, just to be clear: I only used my pond analogy to indicate that the travelin= g wave observed on the surface is caused by the traveling wave in the fluid. In both cases there is a fluid domain with a flexible boundary with a restoring force. I never meant to imply that surface waves on a pond can be used to describe the details of what's going on in the cochlea. The physica= l processes and forces at work in the two cases are completely different. Sorry if this was confusing. Peter 2011/9/22 Matt Flax <flatmax@xxxxxxxx> > Indeed, > > No confusion here by the way ! > > My deep water tsunami analogy is nothing like your pond analogy. Your > pond analogy only really makes sense at the base of the cochlea. > > Travelling waves are generally regarded as having differential pressure > about the BM - pressure waves are generally regarded as having equal > pressure about the BM. The 'reflection' is a minor response (mode) to > the active apex and a major response mode to the active base. > > Our mixed mode Cochlear Amplifier model clearly states this. > > Matt > > On Thu, 2011-09-22 at 09:28 +0200, Peter van Hengel wrote: > > 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 to 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 cause 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 > > starting 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 p= art > > 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 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 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 conc= ept > > from base > > > 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 also > > > 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 opt= imum > > 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 only > > > 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 no= t > > 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=92= t > > 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 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 > > > > > > > > > > > > > > --0016363b81cc02b65604ad842719 Content-Type: text/html; charset=windows-1252 Content-Transfer-Encoding: quoted-printable Hi Matt,<br><br>just to be clear: I only used my pond analogy to indicate t= hat the traveling wave observed on the surface is caused by the traveling w= ave in the fluid. In both cases there is a fluid domain with a flexible bou= ndary with a restoring force. I never meant to imply that surface waves on = a pond can be used to describe the details of what&#39;s going on in the co= chlea. The physical processes and forces at work in the two cases are compl= etely different. Sorry if this was confusing.<br> <br>Peter<br><br><div class=3D"gmail_quote">2011/9/22 Matt Flax <span dir= =3D"ltr">&lt;<a href=3D"mailto:flatmax@xxxxxxxx">flatmax@xxxxxxxx</a>&gt;</= span><br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;borde= r-left:1px #ccc solid;padding-left:1ex;"> Indeed,<br> <br> No confusion here by the way !<br> <br> My deep water tsunami analogy is nothing like your pond analogy. Your<br> pond analogy only really makes sense at the base of the cochlea.<br> <br> Travelling waves are generally regarded as having differential pressure<br> about the BM - pressure waves are generally regarded as having equal<br> pressure about the BM. The &#39;reflection&#39; is a minor response (mode) = to<br> the active apex and a major response mode to the active base.<br> <br> Our mixed mode Cochlear Amplifier model clearly states this.<br> <font color=3D"#888888"><br> Matt<br> </font><div class=3D"im"><br> On Thu, 2011-09-22 at 09:28 +0200, Peter van Hengel wrote:<br> &gt; Hi Matt and list members,<br> &gt;<br> </div><div class=3D"im">&gt; thanks for the support. One small comment to y= our statement that there<br> &gt; are only forward traveling waves. I think much of the confusion stems<= br> &gt; from the fact that the observed motion of the cochlear partition is<br= > &gt; often referred to as the traveling wave. In actual fact this is only a= <br> &gt; &#39;reflection&#39; of the actual wave which is traveling in the flui= d. The<br> &gt; fluid supports waves traveling in both directions, but the unique<br> &gt; properties of the cochlea cause only the appearance of a forward<br> &gt; traveling on the cochlear partition.<br> </div><div class=3D"im">&gt; If one wants to observe the reverse traveling = waves in the cochlea it<br> &gt; is necessary to measure fluid velocity, which I believe is not yet<br> </div><div class=3D"im">&gt; possible. Model calculations clearly show the = reverse traveling wave<br> &gt; and produce results in accordance with data on OAEs (see e.g. the work= <br> &gt; of Mauermann et al or Epp et al). But I&#39;ll (re)check the work of R= en<br> &gt; to make sure I&#39;m not relying only on what I believe to be true ;-)= .<br> &gt; Thanks also to Charles for the support. And many thanks to Dick for<br= > &gt; starting the effort!<br> &gt;<br> &gt; All the best,<br> &gt; Peter<br> &gt;<br> &gt; 2011/9/21 Matt Flax &lt;<a href=3D"mailto:flatmax@xxxxxxxx">flatmax@xxxxxxxx= ee.org</a>&gt;<br> </div><div><div></div><div class=3D"h5">&gt; =A0 =A0 =A0 =A0 I am glad you = brought this up again Peter,<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 I have no problem with the passive travelling wave, ho= wever<br> &gt; =A0 =A0 =A0 =A0 with respect<br> &gt; =A0 =A0 =A0 =A0 to actively induced movements, the latest experimental= data<br> &gt; =A0 =A0 =A0 =A0 shows that<br> &gt; =A0 =A0 =A0 =A0 there are ONLY forward travelling waves (check Ren&#39= ;s<br> &gt; =A0 =A0 =A0 =A0 experiments for<br> &gt; =A0 =A0 =A0 =A0 example).<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 OAEs are generated locally (this is common belief)<br> &gt; =A0 =A0 =A0 =A0 consequently one<br> &gt; =A0 =A0 =A0 =A0 assumes that the basilar membrane is not on the surfac= e, but<br> &gt; =A0 =A0 =A0 =A0 suspended<br> &gt; =A0 =A0 =A0 =A0 inside the pond and the oval/round windows are on the = surface<br> &gt; =A0 =A0 =A0 =A0 of the<br> &gt; =A0 =A0 =A0 =A0 pond.<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 What&#39;s more, if the OHCs in the apex are regarded = as deep<br> &gt; =A0 =A0 =A0 =A0 ocean<br> &gt; =A0 =A0 =A0 =A0 movements, then the waves resemble tsunamis ! Conseque= ntly<br> &gt; =A0 =A0 =A0 =A0 only<br> &gt; =A0 =A0 =A0 =A0 movements near to the shore/surface (the windows) are = easily<br> &gt; =A0 =A0 =A0 =A0 observable<br> &gt; =A0 =A0 =A0 =A0 - the not easily observable being the small movements = of the<br> &gt; =A0 =A0 =A0 =A0 OHCs in the<br> &gt; =A0 =A0 =A0 =A0 apex themselves and the pressure waves (large in poten= tial but<br> &gt; =A0 =A0 =A0 =A0 tiny in<br> &gt; =A0 =A0 =A0 =A0 flux or velocity) in the incompressible fluid.<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 Matt<br> &gt;<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 On Wed, 2011-09-21 at 12:21 +0200, Peter van Hengel wr= ote:<br> &gt; =A0 =A0 =A0 =A0 &gt; Dear dr Heerens and list-members,<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; I hesitate to get involved in this discussion as = I have<br> &gt; =A0 =A0 =A0 =A0 tried to<br> &gt; =A0 =A0 =A0 =A0 &gt; explain the hydrodynamics behind (transmission li= ne) cochlea<br> &gt; =A0 =A0 =A0 =A0 models<br> &gt; =A0 =A0 =A0 =A0 &gt; before in another thread on this list and don&#39= ;t like<br> &gt; =A0 =A0 =A0 =A0 repeating myself.<br> &gt; =A0 =A0 =A0 =A0 &gt; But I feel I have to lend my support the comments= made by<br> &gt; =A0 =A0 =A0 =A0 Dick Lyon.<br> &gt; =A0 =A0 =A0 =A0 &gt; As I have stated before fluid physics states that= a fluid<br> &gt; =A0 =A0 =A0 =A0 domain (such<br> &gt; =A0 =A0 =A0 =A0 &gt; as the cochlea or a pond) with a flexible boundar= y subject<br> &gt; =A0 =A0 =A0 =A0 to a<br> &gt; =A0 =A0 =A0 =A0 &gt; restoring force (such as the aochlear partition o= r the pond<br> &gt; =A0 =A0 =A0 =A0 surface)<br> &gt; =A0 =A0 =A0 =A0 &gt; MUST exhibit &#39;ripples&#39; on the surface. In= the cochlea these<br> &gt; =A0 =A0 =A0 =A0 are<br> &gt; =A0 =A0 =A0 =A0 &gt; refered to as traveling waves. The wave energy is= not<br> &gt; =A0 =A0 =A0 =A0 traveling in the<br> &gt; =A0 =A0 =A0 =A0 &gt; boundary itself but in the fluid. Any attempts to= prove that<br> &gt; =A0 =A0 =A0 =A0 such<br> &gt; =A0 =A0 =A0 =A0 &gt; waves do not exist, or are based on &#39;bad phys= ics&#39;, are<br> &gt; =A0 =A0 =A0 =A0 unfortunately<br> &gt; =A0 =A0 =A0 =A0 &gt; based on a lack of understanding of the fluid mec= hanics.<br> &gt; =A0 =A0 =A0 =A0 &gt; Whether the traveling wave is the only mechanism = responsible<br> &gt; =A0 =A0 =A0 =A0 for<br> &gt; =A0 =A0 =A0 =A0 &gt; transporting sound energy to the hair cells is st= ill a valid<br> &gt; =A0 =A0 =A0 =A0 question,<br> &gt; =A0 =A0 =A0 =A0 &gt; but untill an alternative model produces similar = or better<br> &gt; =A0 =A0 =A0 =A0 results on<br> &gt; =A0 =A0 =A0 =A0 &gt; modeling physiological, pshychophysical and OAE d= ate, I&#39;ll<br> &gt; =A0 =A0 =A0 =A0 stick with<br> &gt; =A0 =A0 =A0 =A0 &gt; the transmission line. Things like pitch percepti= on and the<br> &gt; =A0 =A0 =A0 =A0 missing<br> &gt; =A0 =A0 =A0 =A0 &gt; fundamental can perhaps not be explained purely b= y looking<br> &gt; =A0 =A0 =A0 =A0 at the<br> &gt; =A0 =A0 =A0 =A0 &gt; average excitation caused by the traveling wave, = but I don&#39;t<br> &gt; =A0 =A0 =A0 =A0 think<br> &gt; =A0 =A0 =A0 =A0 &gt; anyone ever claimed they could. In my opinion it = is good to<br> &gt; =A0 =A0 =A0 =A0 develop<br> &gt; =A0 =A0 =A0 =A0 &gt; new theories, but we should attempt to integrate = them with<br> &gt; =A0 =A0 =A0 =A0 existing<br> &gt; =A0 =A0 =A0 =A0 &gt; ones instead of throwing away something that has = proven to<br> &gt; =A0 =A0 =A0 =A0 work.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; Kind regards,<br> &gt; =A0 =A0 =A0 =A0 &gt; Peter van Hengel<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; 2011/9/19 Willem Christiaan Heerens &lt;<a href= =3D"mailto:heerens1@xxxxxxxx">heerens1@xxxxxxxx</a>&gt;<br> &gt;<br> &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Dear Dick Lyon,<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Thank you for your substantial li= st of comments. =A0Of<br> &gt; =A0 =A0 =A0 =A0 course I<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 will reply.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 With pleasure.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 You wrote:<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **Sometimes it&#39;s hard to get = a reaction when you are<br> &gt; =A0 =A0 =A0 =A0 trying to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 replace a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 paradigm, as the silence here ill= ustrates. =A0I didn&#39;t<br> &gt; =A0 =A0 =A0 =A0 really<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 get into the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 new ideas of your book much, but = I have some<br> &gt; =A0 =A0 =A0 =A0 comments on the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 introductory<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 material about why you reject the= current<br> &gt; =A0 =A0 =A0 =A0 paradigm.**<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Your reaction in the first senten= ce is pretty well<br> &gt; =A0 =A0 =A0 =A0 familiar to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 me. It is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 entirely in accordance with the p= rocedure described<br> &gt; =A0 =A0 =A0 =A0 by Thomas<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Kuhn in his<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 world famous 1962 =A0essay:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =93The Structure of Scientific Re= volutions=94<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Besides that: a former colleague = of mine, a highly<br> &gt; =A0 =A0 =A0 =A0 skilled<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 senior professor<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in applied physics, who reviewed = our booklet during<br> &gt; =A0 =A0 =A0 =A0 a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 contribution<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 procedure for a scientific journa= l, quite recently<br> &gt; =A0 =A0 =A0 =A0 gave us the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 verdict that<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 he fully agreed with our argument= s and statements<br> &gt; =A0 =A0 =A0 =A0 and he urged<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the editor<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 to make a full scientific discuss= ion possible for<br> &gt; =A0 =A0 =A0 =A0 our views.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 He also warned<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 me that to be in right is not the= same as to be put<br> &gt; =A0 =A0 =A0 =A0 in right.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 I myself<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 don=92t see all this as a problem= atic issue. It=92s part<br> &gt; =A0 =A0 =A0 =A0 of the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 way messengers<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 or designers of new paradigms are= encountered by the<br> &gt; =A0 =A0 =A0 =A0 mayor<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 supporters of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the competing one. Of course the = scientific<br> &gt; =A0 =A0 =A0 =A0 reputation<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 rankings of so many<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 scientists are involved and in da= nger in case a<br> &gt; =A0 =A0 =A0 =A0 paradigm shift<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 happening.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The only issue that counts for me= is that scientific<br> &gt; =A0 =A0 =A0 =A0 arguments<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 from both<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 sides brought in discussion, veri= fied and weighted<br> &gt; =A0 =A0 =A0 =A0 in a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 careful way must<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 turn the balance. Ignoring irrefu= table arguments<br> &gt; =A0 =A0 =A0 =A0 because they<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 form a thread<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 for the ranking of a scientist ha= s always been<br> &gt; =A0 =A0 =A0 =A0 contra<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 productive for the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 progress in a field of science. H= istory shows many<br> &gt; =A0 =A0 =A0 =A0 of such<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 examples. One of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the most salient among them certa= inly is the<br> &gt; =A0 =A0 =A0 =A0 Copernican<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 revolution.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The result of the second line of = your comment I<br> &gt; =A0 =A0 =A0 =A0 really regret,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 because in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the rest of your writings I clear= ly can see that you<br> &gt; =A0 =A0 =A0 =A0 have<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 apparently<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 missed, misread or misinterpreted= a number of issues<br> &gt; =A0 =A0 =A0 =A0 on<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cardinal points.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Let me discuss your next comment:= <br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **You discuss and reject two wave= concepts: first,<br> &gt; =A0 =A0 =A0 =A0 the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 pressure sound wave<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 that travels so fast that wavelen= gths will always be<br> &gt; =A0 =A0 =A0 =A0 long<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 compared to the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 size of the cochlea, and second, = &quot;capillary&quot; or<br> &gt; =A0 =A0 =A0 =A0 &quot;interfacial&quot;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 waves,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 presumably meaning those water su= rface waves where<br> &gt; =A0 =A0 =A0 =A0 gravity<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 provides the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 restoring force. =A0Of course, ne= ither of these can be<br> &gt; =A0 =A0 =A0 =A0 the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 explanation for<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 how the cochlea works.**<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 I don=92t reject the pressure sou= nd wave concept, at<br> &gt; =A0 =A0 =A0 =A0 least not<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in general. It<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 is of course the vehicle of mecha= nical vibration<br> &gt; =A0 =A0 =A0 =A0 energy and<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 therefore also<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 acoustical vibration energy. How = could an academic<br> &gt; =A0 =A0 =A0 =A0 physics<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 scientist reject<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 that?<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 What I have argued is that for al= l the frequencies<br> &gt; =A0 =A0 =A0 =A0 that can be<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 sensed in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the cochlea even up to 20 kHz cou= nts that the sound<br> &gt; =A0 =A0 =A0 =A0 velocity<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in perilymph =96<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 being 1500 m/s =96 in relation wi= th these frequencies<br> &gt; =A0 =A0 =A0 =A0 result in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 a wave length<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 always larger than 75 mm.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 So therefore this mechanism canno= t contribute to a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 discriminating mechanism<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 for frequency selectivity based o= n traveling waves.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And regarding the =A0&quot;capill= ary&quot; or &quot;interfacial&quot;<br> &gt; =A0 =A0 =A0 =A0 waves I<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 reject: yes indeed<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in quite a number of textbooks I = see the comparison<br> &gt; =A0 =A0 =A0 =A0 of the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 propagation of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 surface waves in a pond with the = slow waves inside<br> &gt; =A0 =A0 =A0 =A0 the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cochlea. It simply<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 is an erroneous analogon. None of= the parameters<br> &gt; =A0 =A0 =A0 =A0 necessary for<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 existence of capillary waves can = be found inside the<br> &gt; =A0 =A0 =A0 =A0 cochlea.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 So neither<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 they can play a role in evoking t= raveling waves that<br> &gt; =A0 =A0 =A0 =A0 have<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 short wavelengths.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 You wrote:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **You also attribute to Lighthill= some strange wrong<br> &gt; =A0 =A0 =A0 =A0 ideas<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 about<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 transmission lines only being abl= e to transmit<br> &gt; =A0 =A0 =A0 =A0 energy near<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 their resonance.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Can you be more specific? =A0The = only lines I describe<br> &gt; =A0 =A0 =A0 =A0 are the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 lines in Fig.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 1. That figure is a reproduction = of the figure in<br> &gt; =A0 =A0 =A0 =A0 Lighthill=92s<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 paper:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Lighthill MJ. (1981) Energy flow = in the cochlea. J<br> &gt; =A0 =A0 =A0 =A0 Fluid Mech<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 106: 149-213.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 I haven=92t attributed strange wr= ong ideas to<br> &gt; =A0 =A0 =A0 =A0 Lighthill. I have<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 studied<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 carefully all the 64 pages =A0of = his paper.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 He starts with a very informative= series of premises<br> &gt; =A0 =A0 =A0 =A0 and I<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cite this part:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 *** With moderate acoustic stimul= i, measurements of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 basilar-membrane<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 vibration (especially, those usin= g a M=F6ssbauer<br> &gt; =A0 =A0 =A0 =A0 source attached<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 to the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 membrane) demonstrate:<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 (i) a high degree of asymmetry, i= n that the response<br> &gt; =A0 =A0 =A0 =A0 to a pure<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 tone falls<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 extremely sharply above the chara= cteristic<br> &gt; =A0 =A0 =A0 =A0 frequency, although<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 much more<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 gradually below it;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 (ii) a substantial phase-lag in t= hat response, and<br> &gt; =A0 =A0 =A0 =A0 one which<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 increases<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 monotonically tip to the characte= ristic frequency;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 (iii) a response to a &#39;click&= #39; in the form of a<br> &gt; =A0 =A0 =A0 =A0 delayed<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 &#39;ringing&#39;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 oscillation at the characteristic= frequency, which<br> &gt; =A0 =A0 =A0 =A0 persists<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 for around 20<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cycles.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 This paper uses energy-flow consi= derations to<br> &gt; =A0 =A0 =A0 =A0 identify which<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 features in a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 mathe=ACmatical model of cochlear= mechanics are<br> &gt; =A0 =A0 =A0 =A0 necessary if it<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 is to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 reproduce these experi=ACmental f= indings.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The response (iii) demands a trav= elling-wave model<br> &gt; =A0 =A0 =A0 =A0 which<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 incorporates an<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 only lightly damped resonance. Ad= mittedly, waveguide<br> &gt; =A0 =A0 =A0 =A0 systems<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 including<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 resonance are described in classi= cal applied<br> &gt; =A0 =A0 =A0 =A0 physics. However,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 a classical<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 waveguide resonance reflects a tr= avelling wave, thus<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 converting it into a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 standing wave devoid of the subst= antial phase-lag<br> &gt; =A0 =A0 =A0 =A0 (ii); and<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 produces a low-<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 frequency cut-off instead of the = high =96frequency<br> &gt; =A0 =A0 =A0 =A0 cut-off (i).<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 By contrast, another general type= of travelling-wave<br> &gt; =A0 =A0 =A0 =A0 system<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 with resonance<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 has become known more recently; i= nitially, in a<br> &gt; =A0 =A0 =A0 =A0 quite<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 different context<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 (physics of the atmosphere). This= is described as<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 critical-layer resonance,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 or else (because the reso=ACnance= =A0absorbs energy)<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 critical-layer absorption.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 It yields a high-frequency cut-of= f; but, above all,<br> &gt; =A0 =A0 =A0 =A0 it is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 characterized by<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the properties of the energy flow= velocity. This<br> &gt; =A0 =A0 =A0 =A0 falls to zero<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 very steeply<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 as the point of resonance is appr= oached; so that<br> &gt; =A0 =A0 =A0 =A0 wave energy<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 flow is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 retarded drastically, giving any = light damping which<br> &gt; =A0 =A0 =A0 =A0 is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 present an<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 unlimited time in which to dissip= ate that energy.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Existing mathematical models of c= ochlear mechanics,<br> &gt; =A0 =A0 =A0 =A0 whether<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 using one-, two-<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0or three-dimensional represent= ations of cochlear<br> &gt; =A0 =A0 =A0 =A0 geometry,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 are analysed<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 from this standpoint. All are fou= nd to have been<br> &gt; =A0 =A0 =A0 =A0 successful<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 (if only light<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 damping is incorporated, as (iii)= requires) when and<br> &gt; =A0 =A0 =A0 =A0 only when<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 they<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 incorporate critical-layer absorp= tion. This resolves<br> &gt; =A0 =A0 =A0 =A0 the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 paradox of why<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 certain grossly unrealistic one-d= imensional models<br> &gt; =A0 =A0 =A0 =A0 can give a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 good<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 prediction of cochlear response; = it is because they<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 incorporate the one<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 dimensional feature of critical-l= ayer absorption.***<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Apparently Lighthill has never co= nsidered the<br> &gt; =A0 =A0 =A0 =A0 possibility that<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the observed<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 movements of the basilar membrane= could be caused by<br> &gt; =A0 =A0 =A0 =A0 another<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 phenomenon<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 than a sound energy transporting = traveling wave.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Your next remark:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **Actually, he showed the opposit= e: =A0that a<br> &gt; =A0 =A0 =A0 =A0 sinusoidal wave<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 will propagate<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 until the point where the transmi= ssion line<br> &gt; =A0 =A0 =A0 =A0 resonance gets low<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 enough to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 match the wave frequency, and at = that point it will<br> &gt; =A0 =A0 =A0 =A0 slow down<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 to zero<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 velocity and die out. =A0This is = not exactly how the<br> &gt; =A0 =A0 =A0 =A0 cochlea<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 works (the BM is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 not very resonant), but not a bad= concept from base<br> &gt; =A0 =A0 =A0 =A0 to near<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the best<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 place.**<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 You say it clearly enough: =A0 = =91It isn=92t a bad concept<br> &gt; =A0 =A0 =A0 =A0 from base<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 to near the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 best place.=92<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 So not having an exact agreement = between theory and<br> &gt; =A0 =A0 =A0 =A0 practice<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 makes the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 underlying hypothesis directly vu= lnerable for<br> &gt; =A0 =A0 =A0 =A0 falsification.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Indeed the cochlea cannot react l= ike that. And I<br> &gt; =A0 =A0 =A0 =A0 want to make<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 this clear by<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the following series of experimen= ts:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Entirely based on the premises of= the new paradigm I<br> &gt; =A0 =A0 =A0 =A0 have<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 described, I now<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 have calculated a number of predi= ctable sound<br> &gt; =A0 =A0 =A0 =A0 phenomena by<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 using the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 following frequencies together wi= th prescribed phase<br> &gt; =A0 =A0 =A0 =A0 relations<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 standard summation procedure to c= ompose a Fourier<br> &gt; =A0 =A0 =A0 =A0 series:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 1:<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A010000 + 10= 004 + 10008 + 10012 + 10016 +<br> &gt; =A0 =A0 =A0 =A0 10020 +<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10024 Hz<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 Where all= the contributions are sine<br> &gt; =A0 =A0 =A0 =A0 functions.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Our paradigm predicts: =A0an undi= sputable beat of 4 Hz<br> &gt; =A0 =A0 =A0 =A0 in a high<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 beep tone.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 2:<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A010000 + 10= 004 + 10008 + 10012 + 10016 +<br> &gt; =A0 =A0 =A0 =A0 10020 +<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10024 Hz<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Where the = contributions are successively<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 alternating sine and<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cosine functions.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Our paradigm now predicts: =A0an = undisputable beat of<br> &gt; =A0 =A0 =A0 =A0 8 Hz in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the same high<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 beep tone.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 3:<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A010000 + 10= 004.0625 + 10008 + 10012.0625 +<br> &gt; =A0 =A0 =A0 =A0 10016 +<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10020.0625 +<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10024 Hz<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Where all = the contributions are sine<br> &gt; =A0 =A0 =A0 =A0 functions.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Our paradigm now predicts: =A0a = =A0beep, in which an<br> &gt; =A0 =A0 =A0 =A0 undisputable<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 beat exists<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 that changes every 8 seconds from= clearly 4 Hz to 8<br> &gt; =A0 =A0 =A0 =A0 Hz and<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 then reverses<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 again to 4 Hz. So the beat patter= n has a period of 8<br> &gt; =A0 =A0 =A0 =A0 seconds<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 caused by the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 systematic mistuning of 1/16 =3D = 0.0625 Hz.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Additional changes in the mistuni= ng, like for<br> &gt; =A0 =A0 =A0 =A0 instance from<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10004.0625 into<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10003.9375 Hz, of either one, two= or three of the<br> &gt; =A0 =A0 =A0 =A0 mistuned<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 frequencies are<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 predicted to give the same result= s in the beat<br> &gt; =A0 =A0 =A0 =A0 pattern as<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 experiment 3.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And actually I want to urge every= body to download<br> &gt; =A0 =A0 =A0 =A0 the software<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 program of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Yves Mangelinckx =A0with which th= ese sound complexes<br> &gt; =A0 =A0 =A0 =A0 can be<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 properly<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 calculated in the form of wav fil= es from the<br> &gt; =A0 =A0 =A0 =A0 following site:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =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><br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 [ NOTE: =A0 =A0The standard setti= ng in the 1/f mode in<br> &gt; =A0 =A0 =A0 =A0 this<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 software program<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 takes care that all the individua= lly primary<br> &gt; =A0 =A0 =A0 =A0 calculated<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 frequencies<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 contribute equal energy to the re= sulting sound<br> &gt; =A0 =A0 =A0 =A0 pressure<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 signal. This<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 condition is very important for t= he influences on<br> &gt; =A0 =A0 =A0 =A0 pitch<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 calculations in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 case higher values of the differe= nces between<br> &gt; =A0 =A0 =A0 =A0 contributing<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 frequencies<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 exist. ]<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 This in order to give the interes= ted reader the<br> &gt; =A0 =A0 =A0 =A0 opportunity to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 falsify or =96<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in case our predictions are corre= ct =96 to verify our<br> &gt; =A0 =A0 =A0 =A0 findings.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And of course I wouldn=92t have g= iven these examples<br> &gt; =A0 =A0 =A0 =A0 if I wasn=92t<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 sure of my<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 statements.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 I can already inform you that ver= ification will be<br> &gt; =A0 =A0 =A0 =A0 the result.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 If you carry out the same series = of experiments with<br> &gt; =A0 =A0 =A0 =A0 a start<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 frequency of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 1000 Hz instead of 10000 Hz, you = will hear the same<br> &gt; =A0 =A0 =A0 =A0 series of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 beat<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 phenomena, but now with the lower= beep of the 1012<br> &gt; =A0 =A0 =A0 =A0 Hz instead<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 of the 10012<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Hz beep.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Even if you go down with the star= t frequency to 200<br> &gt; =A0 =A0 =A0 =A0 Hz or 400<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Hz you will<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 still hear the same beat phenomen= a, but now with the<br> &gt; =A0 =A0 =A0 =A0 low<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 humming tone of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 200 Hz respectively with the one = octave higher<br> &gt; =A0 =A0 =A0 =A0 humming tone of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 400 Hz.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Hence it is a perception phenomen= on that appears all<br> &gt; =A0 =A0 =A0 =A0 over the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 entire<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 auditory frequency range.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And it must be remarked that acco= rding to the<br> &gt; =A0 =A0 =A0 =A0 current hearing<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 theory all<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the used frequencies =96 especial= ly in the higher<br> &gt; =A0 =A0 =A0 =A0 frequencies<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 like in the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 10000 Hz experiments =96 accordin= g to auditory<br> &gt; =A0 =A0 =A0 =A0 experts, and also<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 supported by<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Lighthill, will propagate by mean= s of a traveling<br> &gt; =A0 =A0 =A0 =A0 wave to one<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 and the same<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 location on the basilar membrane.= <br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 If we then still follow the curre= nt hearing<br> &gt; =A0 =A0 =A0 =A0 paradigm, we have<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 to believe<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 that the medley of that seven tot= ally unresolved<br> &gt; =A0 =A0 =A0 =A0 frequencies<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 will be<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 transferred via one and the same = nerve fiber to a<br> &gt; =A0 =A0 =A0 =A0 location in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the auditory<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cortex, where finally out of this= =91Gordian knot of<br> &gt; =A0 =A0 =A0 =A0 stimuli=92 a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 beep with the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 described and also heard beat pat= terns will be<br> &gt; =A0 =A0 =A0 =A0 reconstructed.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Once these beat phenomena are ver= ified as really<br> &gt; =A0 =A0 =A0 =A0 existing for<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 every<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 listener with a reasonable normal= hearing, do you<br> &gt; =A0 =A0 =A0 =A0 agree with<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 me that for<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the current paradigm this is a ve= ry serious anomaly?<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 In my opinion forcing an explanat= ion within the<br> &gt; =A0 =A0 =A0 =A0 framework of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the current<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 paradigm will result in such a co= mplexity that the<br> &gt; =A0 =A0 =A0 =A0 general<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 rule in science,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 known as =A0=91Ockham=92s Razor= =92, to strive to an optimum<br> &gt; =A0 =A0 =A0 =A0 in<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 simplicity will be<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 strongly violated.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Your next remark:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **You conclude that &quot;the exi= stence of two sound<br> &gt; =A0 =A0 =A0 =A0 energy<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 transport phenomena<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 with different transfer velocitie= s within this tiny<br> &gt; =A0 =A0 =A0 =A0 cochlear<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 volume of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 perilymph fluid as suggested by L= ighthill is<br> &gt; =A0 =A0 =A0 =A0 impossible.&quot; =A0Yet<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 all<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 observations do see a slow wave, = much slower than<br> &gt; =A0 =A0 =A0 =A0 the speed of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 sound, and<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 basic mathematical physics of the= same sort that has<br> &gt; =A0 =A0 =A0 =A0 been<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 working well for<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 over 100 years to describe waves = in fluids predicts<br> &gt; =A0 =A0 =A0 =A0 exactly<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 that behavior.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Some may quibble that it has not = been conclusively<br> &gt; =A0 =A0 =A0 =A0 proved that<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the observed<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 slow wave carries energy; but no = workable<br> &gt; =A0 =A0 =A0 =A0 alternative has been<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 put forward,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 and no experiment convincingly co= ntradicts this main<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 hypothesis of the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 current paradigm, as far as I kno= w. =A0I know some on<br> &gt; =A0 =A0 =A0 =A0 this list<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 will probably<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 say I&#39;m wrong, now that I&#39= ;ve opened the door.**<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Do you agree with me that the per= ilymph inside the<br> &gt; =A0 =A0 =A0 =A0 cochlear<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 duct, existing<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 of scala vestibuli and scala tymp= ani, is just moving<br> &gt; =A0 =A0 =A0 =A0 back and<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 forth over<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 distances not exceeding a few mic= rometer?<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 If you admit this fact, you shoul= d also agree with<br> &gt; =A0 =A0 =A0 =A0 me that all<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the known<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 and involved physical quantities = and parameters<br> &gt; =A0 =A0 =A0 =A0 indicate that<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 we are<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 confronted here with the problem = to find the<br> &gt; =A0 =A0 =A0 =A0 hydrodynamic<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 solution for the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 non-stationary small movements of= an incompressible<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 non-viscous fluid in a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 tiny narrow duct.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 According to the rules of physics= it is then<br> &gt; =A0 =A0 =A0 =A0 permitted without<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 any<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 additional constraints to use the= non-stationary<br> &gt; =A0 =A0 =A0 =A0 Bernoulli<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 equation.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The exact and detailed solution o= f this equation I<br> &gt; =A0 =A0 =A0 =A0 can =96 if<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 you wish =96 send<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 you separately.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The result is exactly the mathema= tical expression I<br> &gt; =A0 =A0 =A0 =A0 have used<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 booklet: =A0the pressure decrease= in the perilymph<br> &gt; =A0 =A0 =A0 =A0 duct in front<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 of the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 basilar membrane is everywhere pr= oportional to the<br> &gt; =A0 =A0 =A0 =A0 perilymph<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 velocity<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 squared.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 What leads to the overall result = that the pressure<br> &gt; =A0 =A0 =A0 =A0 stimulus on<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the basilar<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 membrane is proportional to the s= ound energy<br> &gt; =A0 =A0 =A0 =A0 stimulus offered<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 to the ear.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 You further wrote:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 **Yet all obs= ervations do see a slow wave,<br> &gt; =A0 =A0 =A0 =A0 much<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 slower than the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 speed of sound.**<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Indeed, an observation of a =91sl= ow wavy movement=92 and<br> &gt; =A0 =A0 =A0 =A0 the only<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 place where<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 we can observe this is the basila= r membrane.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 It isn=92t the occurrence of a wa= vy movement<br> &gt; =A0 =A0 =A0 =A0 phenomenon that we<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 have to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 discuss. It is the origin of that= =91traveling wave=92<br> &gt; =A0 =A0 =A0 =A0 that we<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 have to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 discover. Is it a vibration energ= y transporting wave<br> &gt; =A0 =A0 =A0 =A0 or is it<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 a phase wave,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 originated out of the manner in w= hich the resonators<br> &gt; =A0 =A0 =A0 =A0 in the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 basilar<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 membrane are grouped?<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 By the way, that is also =96 but = not in an extended<br> &gt; =A0 =A0 =A0 =A0 way =96<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 explained in our<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 booklet. In that chapter of the b= ooklet I describe<br> &gt; =A0 =A0 =A0 =A0 why those<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 =91waves=92 always<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 run from base to apex. It is conf= orm to the peculiar<br> &gt; =A0 =A0 =A0 =A0 mechanics<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 of the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 basilar membrane system that this= phase wave<br> &gt; =A0 =A0 =A0 =A0 behavior is<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 prescribed as it<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 is.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And that mathematical solution fo= r this mechanics<br> &gt; =A0 =A0 =A0 =A0 problem of<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 resonators =96<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in case of the logarithmical freq= uency distribution,<br> &gt; =A0 =A0 =A0 =A0 low near<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the apex to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 high near the base =96 can be cal= culated, as I have<br> &gt; =A0 =A0 =A0 =A0 done,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 analytically for a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 pure sinusoidal tone, which exact= ly results in a<br> &gt; =A0 =A0 =A0 =A0 tonotopical<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 symmetrical<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 envelope of that running phase wa= ve with center<br> &gt; =A0 =A0 =A0 =A0 frequency<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 equal to the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 corresponding resonance frequency= .<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And the running direction of that= phase wave is<br> &gt; =A0 =A0 =A0 =A0 always from<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 base to apex.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Exactly as Tianying Ren has repor= ted in his then<br> &gt; =A0 =A0 =A0 =A0 speech making<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 paper that I<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 have cited:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Ren T. (2002) Longitudinal patter= n of basilar<br> &gt; =A0 =A0 =A0 =A0 membrane<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 vibration in the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 sensitive cochlea. Proc Nat Acad = Sci USA 99:<br> &gt; =A0 =A0 =A0 =A0 17101-6.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The animation of such a phase wav= e can be seen in:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =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><br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 You wrote:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 **It sounds like you&#39;re tryin= g to get away from a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Helmholtz-like conception<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 of resonators or places respondin= g to frequencies,<br> &gt; =A0 =A0 =A0 =A0 and replace<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 it with a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 more time-domain approach that wo= rks for a lot of<br> &gt; =A0 =A0 =A0 =A0 pitch<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 phenomena. =A0But it<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 will work better to put that time= -domain mechanisms<br> &gt; =A0 =A0 =A0 =A0 AFTER the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 what the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 cochlea does. =A0Each hair cell i= s a &quot;tap&quot; on the BM,<br> &gt; =A0 =A0 =A0 =A0 reporting<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 a time-domain<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 waveform as filtered by the trave= ling-wave<br> &gt; =A0 =A0 =A0 =A0 mechanism; that&#39;s<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 where the<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 pitch-processing nonlinear time-d= omain operations<br> &gt; =A0 =A0 =A0 =A0 start...**<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 As you already have indicated in = the beginning, you<br> &gt; =A0 =A0 =A0 =A0 haven=92t<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 studied the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 booklet entirely. I know for sure= that by not<br> &gt; =A0 =A0 =A0 =A0 studying the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 booklet<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 entirely, you have drawn prematur= e conclusions here.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 It is quite on the contrary. I th= ink that I have<br> &gt; =A0 =A0 =A0 =A0 explained<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 clearly enough<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 in the booklet that everywhere al= ong the basilar<br> &gt; =A0 =A0 =A0 =A0 membrane very<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 local<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 resonance with a high quality fac= tor takes place.<br> &gt; =A0 =A0 =A0 =A0 However not<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 on the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 primary sound pressure signal, bu= t on the sound<br> &gt; =A0 =A0 =A0 =A0 energy signal.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Next to that<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the basilar membrane will react e= verywhere =96 but not<br> &gt; =A0 =A0 =A0 =A0 in a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 resonance mode<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 and therefore with much smaller d= isplacements =96 and<br> &gt; =A0 =A0 =A0 =A0 will show<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 a response on<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 other frequency components, inclu= ding utmost low<br> &gt; =A0 =A0 =A0 =A0 frequencies<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 even until<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 stationary pressure signals.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 And for the explanation of our he= aring sense I don=92t<br> &gt; =A0 =A0 =A0 =A0 need a<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 time domain<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 mechanism at all.<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 In the new paradigm, described by= me, from all the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 distinguishable<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 frequencies next of course to the= ir frequency also<br> &gt; =A0 =A0 =A0 =A0 their<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 individual<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 amplitude and phase are transmitt= ed to the auditory<br> &gt; =A0 =A0 =A0 =A0 cortex.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Our brain can directly compare th= e entire frequency<br> &gt; =A0 =A0 =A0 =A0 selected<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 sound energy<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 stimulus with patterns that are s= tored in our<br> &gt; =A0 =A0 =A0 =A0 memory.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Actually I cannot imagine a much = more simpler and<br> &gt; =A0 =A0 =A0 =A0 faster way.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Finally about the definition of O= ckham=92s Razor =96<br> &gt; =A0 =A0 =A0 =A0 also spelled<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Occam =96 I<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 found on the Internet =A0the foll= owing physics<br> &gt; =A0 =A0 =A0 =A0 educational<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 website:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =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><br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 where among others a number of st= ronger but clear<br> &gt; =A0 =A0 =A0 =A0 definitions<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 are given,<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 and I cite:<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 *** If you have two theories that= both explain the<br> &gt; =A0 =A0 =A0 =A0 observed<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 facts, then you<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 should use the simplest until mor= e evidence comes<br> &gt; =A0 =A0 =A0 =A0 along.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The simplest explanation for some= phenomenon is more<br> &gt; =A0 =A0 =A0 =A0 likely to<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 be accurate<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 than more complicated explanation= s.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 If you have two equally likely so= lutions to a<br> &gt; =A0 =A0 =A0 =A0 problem, choose<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 the simplest.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 The explanation requiring the few= est assumptions is<br> &gt; =A0 =A0 =A0 =A0 most<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 likely to be<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 correct.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 . . .or in the only form that tak= es its own<br> &gt; =A0 =A0 =A0 =A0 advice. . .<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Keep things simple! ***<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Within this framework I am convin= ced that I have<br> &gt; =A0 =A0 =A0 =A0 done my<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 utmost best.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 So I am awaiting for a much bette= r explanation for<br> &gt; =A0 =A0 =A0 =A0 the<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 described beat<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 phenomena based on the current he= aring paradigm.<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Kind regards,<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt; =A0 =A0 =A0 =A0 &gt; =A0 =A0 =A0 =A0 Pim Heerens<br> &gt; =A0 =A0 =A0 =A0 &gt;<br> &gt;<br> &gt;<br> &gt;<br> &gt;<br> <br> <br> </div></div></blockquote></div><br> --0016363b81cc02b65604ad842719--


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