Green's Functions and Violin Making

A few years ago, a friend of mine, who is a very accomplished player of the violin & viola and who is an amateur builder of violins & violas, sent me a video on YouTube [LINK] of the violin maker Peter Westerlund showing how to create violins (and violas, by the same logic and with only slightly different overall dimensions) that consistently produce sounds that people well-versed in European classical music judge to be of high quality. Many such people have praised the consistent warm & rich aural tones of violins & violas made in Italy by Andrea Guarneri around 1650 & Antonio Stradivari around 1700, yet it has been difficult for any violin maker to replicate such warm & rich tones in the violins that they have made, in part because there is little scientific consensus about the specific acoustic spectral qualities that make those violins so highly valued. Further complicating matters, as explained in a news article by Science magazine in 2017 [LINK], is the fact that many blind & double-blind studies have left musicians & keen listeners preferring contemporary violins over those made by Stradivari or Guarneri. Even if the instruments by made by Stradivari or Guarneri aren't consistently rated the best, they are rated very highly far more consistently than those made by other violin makers (though this may reflect selection bias in such tests), so there may be merit to considering how to replicate those instruments' aural qualities.

Traditionally, violin makers have carefully studied the exact dimensions, shapes, and materials used in instruments made by Stradivari or Guarneri and done their best to replicate them. However, the resulting aural qualities have typically been judged to be unsatisfactory. This is in various parts due to the effects of aging on the material components of violins (which generally cannot be artificially accelerated), one-off differences in instances of even the same materials used, slight deviations in the craftsmanship, shapes, or dimensions, and other factors that have yet to be explained. This motivated Westerlund (who is probably not the first person to come up with this method) to develop a method to reliably create instruments with highly consistent sounds even if they don't replicate sounds from instruments made by Stradivari or Guarneri per se. The method is as follows. Each violin or viola has a top plate and a back plate, and these are initially constructed separately, joined only later on corresponding sides of the ribs. For each plate, after getting the basic shape & thickness correct, the violin maker should further adjust the shape by tapping or rubbing the plate in various locations, ideally using the same tapping or rubbing motion with the same intensity every time. The violin maker should iteratively shape (by cutting or scraping) at & around those locations of tapping or rubbing and then continue to tap or rub at all locations, until eventually, the tapping or rubbing motion produces approximately the same tone at every location. Once that has been achieved, shaping of the plate is finished.

My background in theoretical & computational nanophotonics from graduate school, even though I was already a few years removed from that even by a few years ago (having changed fields to transportation research after graduate school [LINK]) when my friend shared that video with me, made me interested in trying to mathematically & physically understand why Westerlund's process is successful in creating instruments that have strong internal tonal consistency. However, I wasn't able to come up with a satisfactory answer until much more recently. Follow the jump to see more of my thinking about this, leading to the resolution.

Book Review: "Cosmopolitanism" by Kwame Anthony Appiah

I've recently been able to read Cosmopolitanism by Kwame Anthony Appiah. When I first picked it up, I thought it might be an interesting take on the issues of multiculturalism and immigration that Western societies have had to deal with over the last 2 decades (considering that this book was published in 2006). It actually turned out to be a bit different than I expected, being instead a more abstract philosophical work that lays out the arguments for a certain sort of cosmopolitan worldview and manner of engaging with other people, with these arguments being based on somewhat more abstract discussions of the histories of nations, cultures, and peoples. In particular, the author discusses how cultures have diffused throughout space and time and how people are capable of engaging with different issues and other people from across the world in an intelligent and active manner, so the framing of issues like cultural imperialism/theft or charity for the poorest around the world may end up being counterproductive in the long-term; additionally, the aim of conversation and engagement with strangers should be to reach a mutual understanding and (ideally, though this depends somewhat on the topic at hand) respect for different culture-specific values, because persuasion of people to change such culture-specific values is typically [though not always] a fool's errand. I realize this brief summary doesn't really do the book justice, because it is a rather dense book (at least for a layperson like myself) with so many different issues discussed at varying lengths and levels of abstraction.

Overall, there are a lot of arguments that seem disconnected, especially the anecdotes of his family or his childhood in Ghana (though those were nice to read), and there seem to be a lot of philosophical subtleties that may well have gone over my head, but while each chapter is a nice self-contained explanation of an aspect of cosmopolitanism, the overarching message seems rather muddled (especially comparing the last chapter to everything before it). There are other issues that I have with the book that I'll detail after the jump, but more broadly, I was somewhat disappointed by the ease with which I could use the author's own terms and arguments against the book. That said, I do agree with one main theme, and that is of respectfully engaging with strangers by critically examining "thick" beliefs on their own terms and as they arise from other "thick" & "thin" beliefs (to be explained after the jump), in order to find common ground while also understanding and respecting where differences arise; this is similar to what I learned from the last student-led discussion I attended at the Day of Action on campus in March. I suppose people who are interested in this sort of thing would be drawn to this book anyway, but I wouldn't really recommend this otherwise. Follow the jump to see more of my thoughts on this book.

P2P Is a RESPONSE to a Problem

There's a new article (Jacqui Cheng, Ars Technica) basically summing up a truth about illegal file sharing, with evidence for this as well.
All of the big music stores are now DRM-free. Yet the RIAA has feared massive copyright violations with use of P2P software.
What has this led to? People are legitimately buying DRM-free music and using them appropriately and not illegally downloading them on P2P networks. One reason for this is that P2P networks are meant for large files; music files are small enough to be bought and downloaded off of regular sites.
The bigger reason is that people will legitimately buy content online [I don't know how to make "super-italics" for super-emphasis] IF IT IS EASIER TO DO THAT than to illegally download music. Often, DRM-ed music from P2P sites are of poor quality and may not be the full song, whereas legal music is of great quality and is of full length. Now that legitimate music is DRM-free (while music on P2P sites have cracked DRM), people would rather pay for music than get trashy quality for free.
On the other hand, movies have not gone DRM-free as music has. This means that it is easier to get a lower-quality but unrestricted free copy from a P2P network than it is to get a heavily-restricted, very expensive normal quality copy from another (legitimate) source. The movie industry needs to keep up with the times; given that soon files the size of movies will become very small compared to P2P network capacities (like how music is small compared to current capacities), it would be in the industry's best interests to remove DRM from movies and start selling these movies online.
DRM is a solution to a nonexistent problem, and is in the end a bigger problem than the "problem" it "solves".
Sadly, the RIAA and MPAA will never understand this.