> 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
>