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Re: Traveling waves or resonance?
Andrew, you are right that von Békésy's theory
and other traveling wave theories would have been
known to Gold before 1948, as I've been reminded
by friends already. That would be good to
clarify in your paper. My point remains that he
could not have included active traveling wave
theories in what he was reacting to.
I am surprised you apparently wish to continue
with the broad mechanical tuning idea, and call
for broad neural tuning as well. If you say that
sharp auditory nerve tuning is somehow
imaginary, where does our sharp frequency
discrimination come from? There are many sharp
tuning tips in auditory nerve investigations,
and the standard picture now is that AN tuning
reflects BM tuning [e.g., Khanna & Leonard 1982].
You have introduced the word "broad" into the
discussion, which is not a characterization that
I would use. I completely agree that AN tuning
reflects BM tuning.
When I said that "sharp threshold tuning curves
are an epiphenomenon" I didn't mean that they're
"somehow imaginary", but rather that they are "a
secondary and sometimes unexpected consequence"
of the threshold-type tuning-curve experiments.
My point about "sharp" versus "not very sharp" is
the distinction between an iso-response or
threshold-type tuning curve, which is very sharp,
and an iso-intensity or revcorr-type curve, which
is somewhat less sharp; both are correct
experimental measurements of the same system.
Both BM and AN experiments show the same things,
but the iso-intensity curves are less often
exhibited, so people sometimes mistake the
iso-response curves are being sort of like
"transfer functions" and they therefore make
linear approximations that are way too sharp.
Resonances are generally way too narrow (too
sharp and too symmetric) compared to real data or
to TW models.
I think that your phrase "sharp tuning tips" is a
clue that you be falling for this confusion. The
sharp tips of iso-response or threshold-type
so-called "tuning" curves should not be literally
interpreted as "tuning" in the sense of a linear
filter approximation, since the points on the
curve are measured with very different input
power levels and therefore very different states
of adaptation of the nonlinear system.
My position is that the sharp BM tuning comes
from resonance of OHCs. You think that there are
ways - involving active processes - of making
the TW move all the way from base to apex
without completely dissipating, but only
experiment will decide.
No, that's not what I think. Rather, the TW
moves from base to the point of maximum response,
and not much further. Only the lowest
frequencies, which are not substanially
amplified, make it to the apex.
The TW models have been supported by good 2D and
3D physical modeling for many years. Resonance
models have had a hard time finding either a
physical basis or a mathematical description that
fits the data.
Theories based on analogies with transmission
lines may give the right numbers, but we always
have to ask how apt the analogies are.
The TW theory is not based on that analogy. I
used the analogy just to give you a way to think
about how active processes can lead to high gain
and sharp tuning without resonance.
The combined response of a bank of independent
oscillators looks very much like a traveling
wave: the question is, are the oscillators
independent (resonance) or are they driven
sequentially via coupling (traveling wave)?
I agree, that is a much better thing to argue,
since the answer is likely to be somewhere in
between. The traveling wave models can
acommodate as much local resonance as you want to
put in, of course.
Finally, would Gold agree with me? The question
is unanswerable. But the fact is that the thrust
of his major work was towards a resonance
picture. And together with his prescription for
positive feedback and active processing, he has
been an inspiration to my thinking. In the same
way, I owe a lot to Helmholtz, but whether he
would agree with me is somewhat academic.
I'm with you there. But if you want your theory
to go anywhere, you'll need to put more behind it
in terms of what problems it solves better than
the TW model, or what experimental evidence
supports it. I'm glad you're looking at the
Gold could be wrong. Békésy could be wrong. In
fact, we all could be wrong. Science advances as
fresh ideas are put forward and scrutinised. But
Gold's opinion was "Never judge the strength of
foundation by size of building" [Gold 1989]. In
the end my resonance model, like any other, must
stand or fall on its merits.