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Wasn't v. Helmholtz right?
Dear all who replied,
I greatly appreciate all your valuable contributions. Unfortunately, I was
not yet able to carefully respond to any of them. Nonetheless, the list
might benefit from the most important hints I got privately.
Jont Allen sent me a paper (1) entitled "Cochlear Signal Processing" to
appear in a book to be published in a few month. I am not aware of any
better review of history of one-dimensional cochlear transmission line models.
Jan van Dijk pointed me to a paper (2) in TINS Vol. 21, No. 4, 1998,
159-167 by Nobili et al. The telltale title "How well do we understand the
cochlea?" reminds me to the very insightful Peter Dallos who frankly
admitted he was examining his students every year with the same questions.
No problem, as long as the correct answers were different each time.
Notwithstanding, the paper (2) nicely explains the formation of traveling
waves in a manner that has been accepted for years. It also adds some
interesting statements. For instance, hypothetical 250 kW/kg of OHCs
outperform any technical engine.
Now I am able to draw conclusions with respect to my questions (#134 of the
Wasn't v. Helmholtz right? ----Yes, in the sense, the dominant principle
seems to be pretty local resonance. "Pretty" includes some details of
interaction with the neighborhood like local stimulation by outer hair
cells with non-linear responsiveness, and strong hydrodynamic coupling
being presumably ten times stronger in radial (r) than in longitudinal (x)
direction. Electrical memorizing effects are not excluded. Just a part of
these details has been included in the term micromechanics.
Is the traveling wave the result of energy transmission from base to apex
inside basilar membrane or might it rather be an epiphenomenon, i.e. an
attendant symptom of local resonance? ----No, the amount of energy that
travels within the traveling wave from base to apex inside basilar membrane
is definitely not appreciable. Zwislocki (1946 and 1948) was wrong. The 1D
long wave theory is not appropriate. Present modeling of cochlear mechanics
does not rely on that energy transfer. Instead, they assume vectors of
individual pressure input p(x, t) and undamping (i.e. OHC) input u(y(x),
t). With such inputs, even the 1D active model (see Boston-Univ.) could be
I understand and I respect Antony Locke who expresses the feelings of many
people who possibly depend on outdated textbooks. On the other hand, I do
not consider it justified to take obviously wrong views as a gospel. For
instance, Ohm was wrong in his dispute with Seebeck. Fletcher (1924) was
wrong when the tried to defend Ohm's position, etc.
Having roughly outlined my position with respect to the basic question, I
feel obliged to briefly acknowledge the forward-looking contributions to
the subject by A. Bell, M. Braun, A. Dancer, A. Hudspeth, N. Todd, and R.
Warren. Meanwhile, some doctrines have been put into question, and focus
has shifted on tectorial membrane. I recommend for laymen
Thanks to Stefan Uppenkamp, I understood that the claimed compensation of
cochlear delay obviously happens within the auditory pathway, not within
What about the dispute between Dancer and Ruggero, I realized very good
agreement between measurements by Dancer et al.(1997) and the prediction by
Nobili et al. (1993). So I just quote Dancer: "It is now possible to
re-examine the interpretation of some cochlear physiological phenomena:
i.e., the latency of neural response, of the evoked oto-acoustic emissions
and distortion products..., according to the actual hydromechanical
behaviour of the cochlea."
I quote from (2): "For oscillatory motion, at the characteristic frequency,
the coherence length (that is, the distance over which a transversal
section of the tectorial membrane will appear to move as a single
structure) is about 120 micrometer at the base and 1.2 millimeter at the
apex of the cochlea. Both these figures are in excess of the corresponding
tectorial membrane thickness, implying that it oscillates like a solid mass
attached to the top of the OHC stereocilia bundles."
I further quote from (2) concerning auditory nerve pattern in cats
listening to the vowel a (Secker-Walker and Searle 1990): "The patterning
suggests that groups of fibres respond similarly, even though their
characteristic frequencies might differ by nearly an octave. "
I largely share a comment by Vercoe (in Perception and Cognition of Music)
on this important effect but I suspect that the pattern resulted from some
repetitions. If so, my conclusions were slightly different.
May I ask for hints to some more of such measurements? I merely know Shamma
Thank you very much,