Ron wrote: >Strikes me as smoke and mirrors. Notice that Anderssen built " a >mathematical model". Did he build a real-world model on the bench? >While Anderssen has made certain claims, there is nothing offered by >either Stuart or Anderssen in the way of oscilligrams or other such >results to support their claim. If they had any hard evidence it >would surely have found its way into either brochures or the Stuart >website. But there's nothing, just the claim. A mathematical model - no matter how sophisticated - has little value in characterizing the behaviour of a real physical system unless it is validated. Applied mathematics is not engineering so a mathemaitcal model on its own can "prove" nothing about an engineering system. Validation requires experimentation. You check if your model predictions (abstract mathematics) are consistent with observations (physical behaviour)? Only then can you have any justification for extrapolating and using the model as a predictor under conditions not experimentally tested directly. Without experimentation a mathematical model is only mathematics. As far as I am aware no experimentation was done to validate the string model developed by Anderssen. An equally serious difficulty is that the model itself does not seem to have been published and made available for scrutiny. Last I heard when I contacted the author in 2004 was that he was planning to publish it soon, but so far I haven't seen it appear in any journal and there is nothing available online that I can find. So basically it is a secret model that has not been experimentally tested. Not very convincing for now at least. In this case a model is the icing on the cake. A definitive answer to test all the theories can be had with a very simple experiment using high-speed imaging equipment. The camera has no agenda to prove and shows only what is actually happening. Doing this on a multi-string monochord would be interesting for sure, but not necessarily definitive, because the subject studied must be as close as possible to the real system for the strongest conclusions. That means we need to have a bridge agraffe piano (Stuart or Steingraber) in the same room as the high-speed equipment. Anyone know if there will be one in Rochester? Stephen -- Dr Stephen Birkett Piano Design Lab Department of Systems Design Engineering University of Waterloo, Waterloo ON Canada N2L 3G1 tel: 519-888-4567 Ext. 3792 Lab room E3-3160 Ext. 7115 mailto: sbirkett[at]real.uwaterloo.ca http://real.uwaterloo.ca/~sbirkett
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