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Re: A new paradigm?(On pitch and periodicity (was "correction to post"))
Dear Pim and list members,
my appologies for responding late and briefly. My schedule unfortunately
does not allow me much time for scientific efforts.
First of all let me state that the praise for the book on cochlear
mechanics should go entirely to prof Duifhuis. We did indeed start work
on the book together, but the restrictions that keep me from a lengthy
response also kept me from dedicating enough time to the writing
process. Therefore the book is now the work of prof Duifhuis only and I
can take no credit for it.
In response to your lengthy comments I can only say you seem to know a
great deal about the physics of vibrating fluids and I will not try to
correct you. My knowledge is restricted to computational fluid dynamics
where I got my degree (which is indeed mathematics). So my view is
rather simple: fluid motion is governed by (instationary) Navier Stokes
equations. The work of e.g. Max Viergever has shown that for the largest
part of the cochlea and human frequency range several terms from these
equations can be dropped. The remaining set of equations allows for
traveling waves in the cochlea and the observed wave on the BM. I do not
agree with your view and that of others that there can be no traveling
wave or that the motion caused in the fluid or on the membrane would be
too small to play a significant role, since models based on proper
computational fluid dynamics (on which I may claim to be an expert) show
the traveling wave and a BM motion that is significant. Such models also
correctly predict and describe a large amount of experimental data.
There are things we can not yet model correctly, I have admitted this on
The problem I have with attacks on the traveling wave models (as they
are commonly called, I prefer the term transmission line models) is that
they are usually not based on attempts to simulate the experimental data
using a proper model, but on misconceptions about what these models can
and can not do. In my PhD thesis there is a good example of such a
misconception: the second filter hypothesis. The experiments you are
refering to on retrograde waves and the delays of OAEs also fall in this
category. I wish I had the time to show what the outcome of a
transmission line model would be on simulations of these experiments. I
am sure they would show agreement with the experiments instead of
agreement with the criticism. Please don't take a lack of proof as a
proof of lack.
I (hopefully) end this discussion with the hope that I will some day
find time to show you and others more of what transmission line models
can do, and the hope that you can show me and others what your models
can do. Perhaps we can even some day integrate the two.
All the best,
Op 1-10-2011 13:22, Willem Christiaan Heerens schreef:
> Dear Peter van Hengel and List,
> Peter, my apologies for not responding to your comments earlier but it has
> cost me a lot of time to react in a well-considered way, supported by
> careful explanations.
> And to the members of the AUDITORY List: my apologies for the length of it.
> But first I would like to congratulate you, Peter, with the textbook
> written by you in co-authorship with your former promotor prof. dr. ir. H.
> Duifhuis that was announced to appear on September 1 2011 under the title:
> Cochlear Mechanics
> Authors: Hendrikus Duifhuis & Pieter Willem Jan Van Hengel
> 250 pages | Springer-Verlag New York Inc. | 2011 | September 2011
> ISBN-10: 144196116X & ISBN-13: 978-1441961167
> A brief summary is also given on the Internet and I cite:
> ** The field of cochlear mechanics has received an increasing interest over
> the last few decades. In the majority of these studies the researchers use
> linear systems analysis or linear approximations of the nonlinear (NL)
> systems. Even though it has been clear that the intact cochlea operates
> nonlinearly, lack of tools for proper nonlinear analysis, and widely
> available tools for linear analysis still lead to inefficient and probably
> incorrect interpretation of the biophysics of the cochlea. An example is
> the presumption that a change in cochlear stiffness (at hair cell level)
> must account for the observed change in tuning (or frequency mapping) due
> (e.g.) prestin application. Misconceptions like this need to be addressed
> in a tutorial that is lucid enough to explain basic differences between
> linear and nonlinear cochleae at a graduate level. This book presents a
> useful and mathematically justified/justifiable approach in the main part
> of the text, an approach that will be elucidated with clear examples. The
> book will be useful to scientists in auditory neuroscience, as well as
> graduate students in biophysics/biomedical engineering. **
> I have cited this summary of your textbook because we both have statements
> in common, however on one cardinal issue I see that you and I strongly
> disagree. Actually even almost to the point of insult regarding the other’s
> scientific skills.
> I am pleased to read that you also reject the hypothesis about the role of
> I also want to remark that you and I agree that the intact cochlea operates
> nonlinear and that at the moment tools for proper nonlinear behavior are
> lacking and the linear tools for analysis lead to inefficient and probably
> incorrect interpretation of the biophysics of the cochlea.
> Hence we both opt for at least a quadratic functioning of the cochlea.
> Because this is in general the first next step in non-linear operation.
> But now the subject we seriously disagree about.
> Let me first give a reply on the first item of your supporting comment for
> Dick Lyon:
> You wrote:
> ** 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 cochlear partition or the pond surface) MUST
> exhibit 'ripples' on the surface. **
> I wonder what makes you so sure about that statement. And I elucidate this.
> Ripples on the surface of a pond are actually a combination of transverse
> and longitudinal waves; therefore, the points on the surface follow orbital
> paths. What actually aren’t my words, but the explanation of this wave
> phenomenon you can find in many textbooks.
> You can observe such ripples that start and spread circularly after you
> have thrown a pebble in the pond. That the water particles in the interface
> layer follow orbital paths you can observe as well if in advance you have
> sprinkled small cork particles over the area where the ripples can be
> expected. You clearly see that these particles not only move with the water
> surface in vertical direction, so in line with the restoring force, but
> also in lateral direction, however in time average they remain at their
> lateral location.
> But now the following issue: let me name it ‘oil on the waves’. The ripples
> on the pond, we have observed before, are becoming subject of a relative
> strong damping in case oil is spread as a thin layer on that water surface.
> Whatever the explanation in detail for this damping phenomenon may be, it
> is anyhow clear that the interface conditions are changed substantially by
> that thin oil layer and thus the constraints for evoking ripples are
> changed substantially as well.
> Now you can wonder what will happen if it isn’t a thin oil layer that is
> drifting on the water surface, but a piece of thicker foil with a much more
> internally connected structure. I can guarantee you, and by doing that
> experiment you can verify my statement, that the ripples that will pass
> along that foil will spread according to the wave propagation rules of
> Huygens and the edge of that foil piece will act as the origin of a
> secondary wave front. But the inner part of the foil remains to a high
> extend free of wave motions. And keep in mind that the restoring force –
> the gravitational force – is still present.
> And now the last step in my thoughts about evoking ripples: what will
> happen if we substitute for the air on top of that foil another fluid with
> almost identical qualities as the water below the foil? There won’t be a
> ripple left at all. All the conditions necessary for the ripple phenomenon
> do not exist anymore.
> So I have a question for you:
> Isn’t that a valid reason for my doubts about your statement that a fluid
> domain under the condition like you have formulated above, with the only
> condition that a flexible boundary is subject to a restoring force MUST
> exhibit 'ripples' on the surface?
> You can ask me the question: on what grounds are you arguing? Do you have
> the skills for this scientific subject?
> Well let me inform you that all the above mentioned boundary interface
> issues were part of my research that lead to my masters degree in 1967. For
> that research project in that time I had to follow the course called ‘Hydro-
> dynamical Engineering’. A course really loaded with the equations of Gauss,
> Green and Navier-Stokes and even more. But also solutions of Laplace’s
> equation in case of potential flow.
> Later in my career that same knowledge, together with a post graduate study
> of ‘Special Function Theory’, made it possible for me to publish a series
> of papers about the analytical solution of Laplace’s equation in toroids
> and cylinders with several types of boundary conditions.
> I am informed that you have a masters degree in mathematics, not in
> physics, so if you are interested, I can give you full references, or even
> scanned copies of those papers. These analytical mathematical solutions can
> also play a role in achieving reliable rules of thumb for instance in the
> case of dimensioning potential distributions in cochlear implant research.
> And finally it was also part of the basis for the academic courses I gave a
> number of years with subjects like ‘Introduction to Electricity and
> Is all this detailed CV information for you satisfactory enough to take my
> contributions in this subject serious?
> I have followed the indication you gave me in the beginning of your reply
> to me:
> ** 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. **
> So I found out that you are familiar with this subject. You explicated that
> in the discussion thread of March 2010:
> ** In response to Martin Braun I have a question how there can be a motion
> of fluid without a pressure change, or a sound wave without a pressure
> change? The fluid mechanics I know (Bernoulli etc) states that any motion
> of fluid is always linked to a pressure gradient, therefore pressure
> difference, and I thought a sound wave was defined as pressure differences
> traveling. **
> Correct me if I interpret your explanation wrong: do you really mean
> Bernoulli related to a pressure gradient? And then a gradient in the
> direction of the flow?
> About the pressure gradient you are right, but only in the case of a
> viscous flow. Because in that case the internal friction forces result in a
> pressure gradient in the flow direction. For a tube with circular cross
> section this negative gradient – the pressure drop per unit of length – is
> proportional to the coefficient of viscosity multiplied by the volume flow
> and divided by the fourth power of the tube diameter. In hydrodynamics
> this is well known under the name: ‘flow relation of Hagen-Poiseuille’. And
> this relation is valid for a laminar flow in the tube, which exists if the
> Reynolds number – the ratio between inertia forces and friction forces – is
> less than 2000.
> In case of flow in a tube under the material conditions incompressible and
> non-viscous and a rotation free flow condition, for stationary flow counts
> the Bernoulli equation. In a horizontal orientated tube gravity doesn’t
> play a role, what leads to the well known equation: the decrease of the
> overall existing internal pressure is proportional to fluid velocity
> And as you can see in my attachment: in the case of a non-stationary flow
> with all other conditions the same as above, that overall pressure inside
> the tube – and thus also on its boundaries – is proportional to the time
> dependent fluid velocity squared.
> There doesn’t exist a pressure gradient inside that fluid column, as long
> as the area of the cross section remains the same. If the diameter of the
> cross section changes as function of the distance measured along the tube
> axis, while the shape of the cross section remains the same, the fluid
> velocity will be reciprocal to the squared diameter and consequently the
> local pressure decrease changes with the fourth power of that diameter. So
> if the duct has a tapered shape the pressure distribution along the duct
> shows a small pressure drop in the wider areas and an increasing pressure
> drop in narrower areas. However that isn’t the pressure gradient that acts
> as the driving force you have in mind, because this pressure distribution
> isn’t the cause of the flow in the fluid but the result of it.
> In that same contribution in March 2010 you stated:
> ** All I have said about the traveling wave was based on a fluid with a
> flexible boundary which has a restoring force. If the fluid is moved, in
> this case you will always get a traveling wave. **
> And exactly this statement I do not only call in question, I even reject
> this traveling wave hypothesis. It isn’t a law of Medes and Persians that
> you always get a traveling wave in case the fluid moves in presence of a
> restoring force in the wall of the involved duct.
> Referring to the extensive research on this topic by Shankar and Kumaran [1
> & 2] and making an indicative calculation example in case of a 2 micrometer
> total displacement of the oval window on a 20 kHz pure tone signal, we get
> as a result for the maximum perilymph velocity 0.012 m/s. And with a 20
> micrometer oval window displacement on a 1 kHz pure tone this maximum
> perilymph velocity is 0.006 m/s.
> These velocities are far too low to generate periodic instabilities that
> can lead to what can be observed as a traveling wave. Neither in the fluid
> nor in the wall.
> Just follow a while Albert Einstein – a real wise man – with his
> quote: "Imagination is more important than knowledge".
> So please use your imagination. And then, are you really convinced that in
> a fluid column that is wiggling in its length direction with hardly
> observable displacements – and if so even with serious measuring problems,
> even with a high resolution microscope – that wiggling will generate
> pressure disturbances in the size of a few millimeters which propagate in
> that fluid column? Just because your mathematical model prescribes these
> See also the references:
> 1. Shankar V, Kumaran V. (1999) Stability of non-parabolic flow in a
> flexible tube. J. Fluid Mech. 395: 211- 236.
> 2. Shankar V, Kumaran V. (2000) Stability of fluid flow in a flexible tube
> to non-axisymmetric disturbances. J. Fluid Mech. 407: 291- 314.
> While for the flow, inside the perilymph duct, not just one single but all
> conditions for a potential flow and thus for the analytical solution
> according to Bernoulli’s relation for non-stationary flow are fulfilled.
> And it is that solution based on the sound and solid use of hydrodynamic
> rules and laws that is the straight forward outcome that I give in the
> For me actually this was both a renewed confrontation with the knowledge
> that I had gathered now 46 years ago and the joyful experience that I
> didn’t lost my touch on hydrodynamics.
> And that result can be summarized in the ultimate short statement that the
> changes in the internal pressure everywhere in the perilymph – that moves,
> or better wiggles, on the rhythm of the sound pressure in front of the
> eardrum – are proportional to the corresponding sound energy.
> The change in the internal pressure is a decrease proportional to the time
> derivative of the sound pressure signal squared.
> Based on that result we have done the series of sound experiments that are
> described in Chapter 3 of our booklet and that are explained there in
> detail in the Appendices. Together with the offered downloadable
> calculation program for composing those sound complexes, the inquisitive
> reader can verify all our results.
> In my reply to Dick Lyon of Monday the 19th of September 2011 I suggested
> the experiments with the composed beat series of seven pure tones, based on
> the 10 kHz frequency; 4 Hz spacing in frequency; a 0.0625 Hz detuning on
> the 2nd 4th and 6th frequencies and all sine or alternating sine cosine
> In all these proposed experiments the calculation of the different
> contributions to the sound energy frequency spectrum resulted per
> experiment in exact predictions of the final beat rhythm.
> And now I want to address both a comment and a question to you about your
> provocative statement:
> **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.**
> My comment:
> The non-stationary potential flow according to Bernoulli in the perilymph
> duct, like I have calculated, includes that everywhere inside this fluid
> there exist the balance between the kinetic energy represented by the
> expression ‘1/2 rho v^2’ – or for the total perilymph volume V ‘1/2 m v^2
> and the decrease in potential energy, given by the expression : ‘– V delta
> Here rho is the density of the fluid; v the fluid velocity; delta p the
> pressure difference and m the mass of the fluid column.
> So also here the sound energy signal is present inside the perilymph fluid.
> However not in the form of an assumed traveling wave, but as a uniform
> pressure stimulus all over the volume.
> And therefore all the existing Fourier frequency components in the sound
> energy signal are present inside the perilymph to stimulate the basilar
> membrane including their relative amplitudes and their relative, but
> extremely precise, phase relations.
> And it is this concept that makes it possible to calculate all the
> phenomena heard in the sound experiments, even if they are as weird as the
> sound perceptions I gave in the 10 kHz example.
> And now my question to you:
> Are you still fully convinced that my contribution must be categorized as
> the next fruitless attempt of someone who thinks he can contribute on your
> high scientific level?
> Since there hasn’t appeared a single reaction about it on this AUDITORY
> List, I really wonder if there is anybody on this List who has done the
> experiments that I have described and who has verified the results
> belonging to them for satisfying his/her curiosity. I have more than enough
> testimonies from independent examiners who confirm my claims. But I hardly
> can imagine that none of the auditory experts can’t hear them.
> What for instance is observed from the following combinations of
> 10000+10004.0625+10008+10012.0625+10016+10020.0625+10024 Hz
> 2000+2004.0625+2008+2012.0625+2016+2020.0625+2024 Hz
> 400+404.0625+408+412.0625+416+420.0625+424 Hz
> having all sine or all cosine contributions, is that they will have an
> average frequency – 10012; 2012 respectively 412 Hz – with a beat rhythm
> 4 – 8 – 4 – 8 – 4 – 8 – 4 – 8 – 4 Hz within 32 seconds, so a period of 8
> While having alternating sine – cosine – sine … or cosine – sine – cosine
> … contributions, they get a beat with the opposite sequence in the rhythm
> 8 – 4 – 8 – 4 – 8 – 4 – 8 – 4 – 8 Hz within 32 seconds, so with a period
> of 8 seconds.
> In these series you can of course try to attribute the beat phenomena
> to ‘special combinations’ of these frequency contributions to eliminate
> the problems that arise when the traveling wave model is applied.
> Well in order to enervate these suggestions in advance, let me add another
> experiment with which this is absolutely impossible.
> Let us chose the following frequency contributions:
> A series of five tones existing of:
> 8009+8011+8013+8015+8017 Hz
> with a minimal difference frequency of 2 Hz.
> Where the first, second and fifth contributions are prime numbers, the
> 8013 Hz contribution is the product of two prime number: 3 x 2671, and the
> 8015 Hz contribution is the product of three prime numbers: 5 x 7 x 229.
> These integer frequency contributions only have 1 Hz as fundamental.
> And a series of five tones existing of:
> 7499+7501.0625+7503.125+7505.1875+7507.25 Hz
> with a difference frequency of 2.0625 Hz. Again no fundamental.
> If all those contributions have sine or cosine functions the beat
> phenomenon is given by: a high beep tone with a dominant beat rhythm of:
> 2 – 4 – 2 – 4 – 2 Hz within 32 seconds, so with a period of 16 seconds
> that is mixed with a weaker 6 Hz beat rhythm.
> If you modify each of the two frequency series in sine–cosine–sine–cosine–
> sine or cosine–sine–cosine–sine–cosine contributions, you will hear a beat
> phenomenon in the same high beep tone, but now with a beat rhythm of 4 –
> 8 – 4 – 8 – 4 – 8 – 4 – 8 – 4 Hz within 32 seconds, so with a period of 8
> seconds. Now not only the 2 Hz beat, but also the 6 Hz beat is disappeared.
> Now each series apart produce a pure beep tone with a 2 Hz, respectively a
> 2.0625 Hz beat, in case of all sine or cosine contributions and a 4 Hz
> beat respectively a 4.125 Hz beat in case of alternating sine–cosine–sine–
> cosine–sine or cosine–sine–cosine–sine–cosine contributions.
> If we calculate the sound energy frequency spectrum, we can observe that
> only the series of difference frequencies 2.0625 + 4.125 + 6.1875 + 8.25
> Hz, respectively 2 + 4 + 6 + 8 Hz, in the pair by pair combined situation
> can generate the beat phenomena we can hear.
> For the 10 kHz experiments the 0.0625 Hz detuning means that there exists
> an accuracy in the periodicity pattern of 6.25 parts per million.
> I cannot believe that these salient auditory perception results for each
> chosen average frequency over the entire auditory frequency domain are
> heard by everybody else except the auditory experts, being the members of
> this AUDITORY List.
> Neither I can believe that the experiments mentioned above fit well in the
> transmission line concept, of which you are an adept.
> Peter you wrote:
> ** 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. **
> Of course you can. Probably I would have done the same if I were as
> convinced as you about the transmission line calculation model that you are
> applying. And what then counts is that such calculation models must be in
> agreement with the rules and laws of physics.
> You also replied with:
> ** 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. **
> No indeed, but do you acknowledge that it is strange indeed that we have
> to apply a relative great number of different models with in many cases
> significantly restricted validity domains for the description of all the
> hearing phenomena? And yet there are still a substantial number of
> phenomena that cannot be explained or that are falling in the category
> In all widely explored fields of science scientists always strive for a
> consistent theoretical structure that covers the concerned scientific field
> as much as possible as a whole. And all the scientific contributions in the
> auditory field, I have studied so far, give me the impression that this is
> also the goal of all the serious workers in auditory science.
> Therefore I don't quite understand your last remark in the support of Dick
> **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.**
> That’s the way science can develop according to Karl Popper. Small steps in
> a row.
> Let me give you some examples to show you what the consequences of your
> statement imply.
> A scientific revolution was necessary to step over from the geocentric
> world view to the Copernican heliocentric world view, since both theories
> are incommensurable.
> And Einstein’s theory of relativity cannot be integrated in the physics
> theory of Newton.
> And there are many, many more examples like these to give.
> If the constraint for new scientific work would be dictated as you suggest:
> restricted to investigations that fit within the existing knowledge, I fear
> that scientific progress will become very poor.
> In your reply to Matt Flax you wrote:
> ** just to be clear: I only used my pond analogy to indicate that the
> traveling 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
> physical processes and forces at work in the two cases are completely
> different. Sorry if this was confusing. **
> Well now you are arguing in the same way as Nobel prize laureate Richard
> Feynman did. He warned that using the ripples in a pond as example for
> other wavy phenomena is mostly wrong, because of the unnoticed complexity
> in this water wave phenomenon.
> And then on the comment of Matt, I cite here:
> ++ 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). ++
> You replied to him:
> ** 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.**
> Yes that is commonly supposed to happen. However experimental data of
> Tianying Ren – at first flawed by other cochlear scientists – but quite
> recently confirmed by experiments with a different experimental method
> under the guidance of De Boer and Nuttall, show that no backwards traveling
> waves can be found.
> After that surprising discovery De Boer expressed in public that this was a
> clear anomaly and this problem should be solved in order to repair the
> existing OAE theory that uses the backward traveling wave concept and he
> and his coworkers have started an investigation with a concept that
> hypothesizes, that evoked forward traveling waves in the cochlear duct will
> transfer the OAE stimulus from the scala tympani to the eardrum.
> Ren T. (2004) Reverse propagation of sound in the gerbil cochlea. Nature
> Neuroscience 7, 333 - 334
> De Boer E, Zheng J, Porsov E, Nuttall AL. (2008) Inverted direction of wave
> (IDWP) in the cochlea. JASA 123(3):1513-1521.
> He W, Fridberger A, Porsov E, Ren T. (2010) Fast reverse propagation of
> sound in the living cochlea. Biophys J. Jun 2;98(11): 2497-505.
> Your reply to Matt:
> ** 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 ;-).**
> Yes and that is precisely the problem: ‘model calculations clearly show the
> reverse traveling wave’. But in reliable experiments in practice, [ Ren, De
> Boer et.al. ] they aren’t observed. Only forward traveling waves along the
> basilar membrane are found.
> In the summary of the 3rd mentioned paper [He, Fridberger, Porsov and Ren]
> there are given a number of interesting conclusions:
> -- … However, the fundamental question of how the otoacoustic emission
> exits the cochlea remains unanswered. In this study, emissions were
> provoked by two tones with a constant frequency ratio, and measured as
> vibrations at the basilar membrane and at the stapes, and as sound pressure
> in the ear canal.
> The propagation direction and delay of the emission were determined by
> measuring the phase difference between basilar membrane and stapes
> These measurements show that cochlea-generated sound arrives at the stapes
> earlier than at the measured basilar membrane location. Data also show that
> basilar membrane vibration at the emission frequency is similar to that
> evoked by external tones. These results conflict with the backward-
> traveling-wave theory and suggest that at low and intermediate sound
> levels, the emission exits the cochlea predominantly through the cochlear
> fluids. …--
> Because both the sound related vibrations of the stapes apparently started
> earlier than the corresponding basilar membrane movements and the basilar
> membrane movements appear to be similar to movements evoked by external
> tones, we might also draw the conclusion that the otoacoustic signal is
> generated in the stapes and then as a normal sound signal transferred to
> the basilar membrane.
> Let us be wise. The physics society is already thrown into commotion by the
> news that CERN announced the measurement of neutrino’s running faster than
> light. We mustn’t add the information that acoustic vibrations even travel
> back in time, because the OAE’s evoked in the cochlea are reaching the
> stapes earlier than the location from where they are assumed to come.
> This divergence between predicting models and reliable verifiable
> experiments shows that the traveling wave model might be seriously wrong.
> Finally I will end with the quote of sir James Lighthill, that forms the
> beginning of the Memorial Tribute dedicated to him and written by Lokenath
> Debnath in 1998, the year Lighthill passed away.
> [See also: http://www.emis.de/journals/HOA/IJMMS/22/4667.pdf ]
> “... as Sir Cyril Hinshelwood has observed ... fluid dynamicists were
> divided into hydraulic engineers who observed things that could not be
> explained and mathematicians who explained things that could not be
> James Lighthill
> This because it expresses my impression very well for the moment.
> Kind regards,
> Pim Heerens