Subject: Re: A new paradigm?(On pitch and periodicity (was "correction to post")) From: Willem Christiaan Heerens <heerens1@xxxxxxxx> Date: Mon, 19 Sep 2011 06:07:57 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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