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Re: Traveling waves or resonance?


You wish to discount Gold's bold 1948 claim that "previous theories of hearing are considered, and it is shown that only the resonance theory of Helmholtz... is consistent with observation", thinking perhaps he wasn't targeting von Békésy's traveling wave theory. The evidence appears to be otherwise.

1. It is a mistake to think that, because von Békésy's book only appeared in 1960, Gold didn't know about TW theory in 1948. 'Experiments in Hearing' is actually a collection of nearly 50 papers published by von Békésy between 1928 and 1958, and as David Kemp recounts in his recent historical piece [Kemp 2003], "von Békésy first explained how sound created travelling waves on the basilar membrane in the 1940s".

2. Gold met Békésy at Harvard and tried to persuade him of the errors in his TW model [described in Gold 1987]. Scaling effects in his physical models were wrong, and there was the problem of the enormous neural discrimination needed for a broadly tuned system to locate the displacement peak, an impossible task in the inevitable presence of noise. 

3. Gold was the kind of person who said what he thought, so he probably meant what he wrote in his abstract. He is quoted as saying, "In choosing a hypothesis there is no virtue in being timid". At the same time, his lack of timidity may have led to his 1948 paper never seeing the light of day, as we now know that one reviewer recommended against its publication [Zwislocki 2002, p.176].

While von Békésy's name is now almost synonymous with traveling waves, we should appreciate that the theory goes back well before him, although it is true he championed the idea and was the first to see it in the cochlea. In his book and Nobel Prize address he refers to his predecessors who first put forward the traveling wave idea: Hurst 1895, Bonnier 1895, ter Kuile 1900.

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].

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. Theories based on analogies with transmission lines may give the right numbers, but we always have to ask how apt the analogies are. 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)?

It is true that in 1949 Gold was working with a mathematician, Noble, on a transmission line model of the cochlea [Gold 1989], suggesting he was entertaining some sort of traveling wave theory, but since this work was never published we can't gauge the strength of it. Reading that manuscript would indeed be illuminating.

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.

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.


Gold (1987). Historical background to the proposal, 40 years ago, of an active model for cochlear frequency analysis. In: Cochlear Mechanisms, ed JP Wilson & DT Kemp. Plenum, NY, 299-305.
Gold (1989). New ideas in science. J. Sci. Exploration 3, 103-112.
Kemp (2003). 25 years of progress with OAEs: the inside story. Presentation to ASHA conference, Chicago, November 2003 [on ASHA web site].
Khanna, SM & Leonard, DGB (1982). Basilar membrane tuning in the cat cochlea. Science 215, 305-306.
Zwislocki, JJ (2002). Auditory Sound Transmission: An Autobiographical Perspective. Erlbaum, Mahwah, NJ.

Andrew Bell
Research School of Biological Sciences
The Australian National University
Canberra, ACT 0200, Australia
T: +61 2 6125 9634
F: +61 2 6125 3808

-----Original Message-----
From: AUDITORY Research in Auditory Perception [mailto:AUDITORY@LISTS.MCGILL.CA] On Behalf Of Richard F. Lyon
Sent: Saturday, 16 October 2004 3:27 PM
Subject: Re: [AUDITORY] Traveling waves or resonance?

>Some years back this list began a discussion on the relative virtues of
>viewing the cochlea as driven by traveling waves or resonance. Happily,
>progress has been made in my endeavours to revive a resonance theory of
>hearing and an approachable discussion piece on the subject has just been
>published in PLoS Biology. The reference is
>Bell A (2004) Hearing: Travelling Wave or Resonance? PLoS Biol 2(10): e337.
>The open-access, full-text article is at


That is indeed an approachable piece, very well written and produced.
But I'd like to disagree with it anyway.  A few points for now.

First, you say of Gold that "In fact, the abstract of his 1948 paper
declares that Œprevious theories of hearing are considered, and it is
shown that only the resonance theory of HelmholtzŠ is consistent with
observation¹."  But did he mean to include the traveling wave theory
in that?  Von Békésy¹s book was 1960, so he certainly wasn't reacting
to that.  And nodoby had an active traveling wave theory yet, so he
couldn't be including there.  And many ohters have concluded that the
theory of Helmholtz is NOT consistent with what we know of hearing.

Second, the "regenerative" idea is not the only way to get a big
active gain. In fact, it has the trouble of being only an extremely
narrow-band way to get gain. The first really high-gain
high-bandwidth electronic amplifier was the invention of Rudy
Kompfner and John Pierce known as the travelling-wave-tube amplifier.
It used a travelling wave in an active medium (a beam of moving
electrons in this case) to get high gain over a wide band, without
feedback. Take a look at that idea, and I think you'll see that it's
a better analog of the cochlea than the idea of "resonance" is.

Third, sharp threshold tuning curves are an epiphenomenon.  If you
look at output of a hair cell or neuron versus frequency, for a constant
input power or amplitude or velocity or anything else, you do NOT
get a very sharp curve.  Von Békésy¹s "lateral inhibition" went a long
way to explaining that apparent discrepancy, though it took some years
of interpretation.

I think Gold was brilliant and way ahead of his time, but I'm not
sure he would take the position that you're taking.

Dick Lyon