Subject: Re: Traveling waves or resonance? From: "Richard F. Lyon" <DickLyon(at)ACM.ORG> Date: Sun, 17 Oct 2004 20:57:34 -0700Andrew, 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. > >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. 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 question. Dick