>         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:
>
>         “The Structure of Scientific Revolutions”
>
>         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’t see all this as a problematic issue. It’s part of the
>         way messengers
>         or designers of new paradigms are encountered by the mayor
>         supporters of
>         the competing one. Of course the scientific reputation
>         rankings of so many
>         scientists are involved and in danger in case a paradigm shift
>         is
>         happening.
>
>         The only issue that counts for me is that scientific arguments
>         from both
>         sides brought in discussion, verified and weighted in a
>         careful way must
>         turn the balance. Ignoring irrefutable arguments because they
>         form a thread
>         for the ranking of a scientist has always been contra
>         productive for the
>         progress in a field of science. History shows many of such
>         examples. One of
>         the most salient among them certainly is the Copernican
>         revolution.
>
>         The result of the second line of your comment I really regret,
>         because in
>         the rest of your writings I clearly can see that you have
>         apparently
>         missed, misread or misinterpreted a number of issues on
>         cardinal points.
>
>         Let me discuss your next comment:
>
>         **You discuss and reject two wave concepts: first, the
>         pressure sound wave
>         that travels so fast that wavelengths will always be long
>         compared to the
>         size of the cochlea, and second, "capillary" or "interfacial"
>         waves,
>         presumably meaning those water surface waves where gravity
>         provides the
>         restoring force.  Of course, neither of these can be the
>         explanation for
>
>         how the cochlea works.**
>
>         I don’t 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 –
>         being 1500 m/s – 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’s
>         paper:
>
>         Lighthill MJ. (1981) Energy flow in the cochlea. J Fluid Mech
>         106: 149-213.
>
>         I haven’t 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 Mössbauer 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¬matical model of cochlear mechanics are necessary if it
>         is to
>         reproduce these experi¬mental 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 –frequency 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¬nance  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:   ‘It isn’t a bad concept from base
>         to near the
>         best place.’
>         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 = 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 –
>         in case our predictions are correct – to verify our findings.
>
>         And of course I wouldn’t have given these examples if I wasn’t
>         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 – especially in the higher frequencies
>         like in the
>         10000 Hz experiments – 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 ‘Gordian knot of stimuli’ 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  ‘Ockham’s Razor’, to strive to an optimum in
>         simplicity will be
>         strongly violated.
>
>         Your next remark:
>
>         **You conclude that "the existence of two sound energy
>         transport phenomena
>         with different transfer velocities within this tiny cochlear
>         volume of
>         perilymph fluid as suggested by Lighthill is impossible."  Yet
>         all
>         observations do see a slow wave, much slower than the speed of
>         sound, and
>         basic mathematical physics of the same sort that has been
>         working well for
>         over 100 years to describe waves in fluids predicts exactly
>         that behavior.
>         Some may quibble that it has not been conclusively proved that
>         the observed
>         slow wave carries energy; but no workable alternative has been
>         put forward,
>         and no experiment convincingly contradicts this main
>         hypothesis of the
>         current paradigm, as far as I know.  I know some on this list
>         will probably
>
>         say I'm wrong, now that I've opened the door.**
>
>         Do you agree with me that the perilymph inside the cochlear
>         duct, existing
>         of scala vestibuli and scala tympani, is just moving back and
>         forth over
>         distances not exceeding a few micrometer?
>
>         If you admit this fact, you should also agree with me that all
>         the known
>         and involved physical quantities and parameters indicate that
>         we are
>         confronted here with the problem to find the hydrodynamic
>         solution for the
>         non-stationary small movements of an incompressible
>         non-viscous fluid in a
>         tiny narrow duct.
>         According to the rules of physics it is then permitted without
>         any
>         additional constraints to use the non-stationary Bernoulli
>         equation.
>
>         The exact and detailed solution of this equation I can – if
>         you wish – 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 ‘slow wavy movement’ and the only
>         place where
>         we can observe this is the basilar membrane.
>
>         It isn’t the occurrence of a wavy movement phenomenon that we
>         have to
>         discuss. It is the origin of that ‘traveling wave’ 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 – but not in an extended way –
>         explained in our
>         booklet. In that chapter of the booklet I describe why those
>         ‘waves’ 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 –
>         in case of the logarithmical frequency distribution, low near
>         the apex to
>         high near the base – 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’t
>         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 – but not in a
>         resonance mode
>         and therefore with much smaller displacements – 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’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’s Razor – also spelled
>         Occam – 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
>