## Violin Social Experiment

Most people seem to think of street performers as poor artists trying to eek out a living. In 2008, the Washington Post set out to prove just how little people really paid attention to public performances by enlisting the help of Joshua Bell, one of the world’s top violinists. Armed with a multi-million dollar Stradivarius from 1713, Bell performed in the L’Enfant Plaza subway station and played a variety of pieces for 43 minutes to include Johann Sebastian Bach’s Chaconne. As one of the world’s foremost musicians playing one of the most challenging pieces on a priceless instrument … he made $32.17 while passed by nearly everyone at rush hour. The experiment eventually won a Pulitzer Prize for its exposure of our collective, artistic ignorance.

It does make one wonder, are the masses **stupid for not recognizing aural beauty** or is it beautiful **because the elites tell us it is**?

Similarly tagged OmniNerd content:

- Color Coded School Performance, by VnutZ over 3 years ago
- Music Purchase Log: December 2008, by Brandon over 6 years ago
- Keeping Up with Music, by Brandon about 7 years ago
- Music Review: September 2007, by Brandon over 7 years ago

## WTF? by Occams

As an experiment it is invalid as a test of musical appreciation for many reasons.

*The location is not conducive to the enjoyment of music;

*The acoustics were terrible;

*there was no seating; and

No one claims that classical violin solos are popular music today.

It beggars belief that such an absurd stunt could have won a Pulitzer.

## RE: WTF? by VnutZ

Actually, the article states the acoustics were surprisingly good.

## RE: WTF? by Occams

the acoustics were surprisingly good.

Perhaps so, but that would indeed be surprising because were hard surfaces everywhere, and the sound through the recording and You Tube was harsh.

My main problem with the story is straining to believe that the prestigious Pulitzer prize judges would regard it as being a serious social experiment. Even arty people should have more practical sense than that.

## Inherent Beauty or Explicit Beauty by VnutZ

I still the question stands … is something as difficult as Chacune played by a master on beautiful automatically or because we are told it is?

Despite the fact that all of the passerbys were in a rush to get somewhere (it’s arguable how much of a rush any of us are really in), very few stopped to admire what was played. Presumably, we [OmniNerds] have heard buskers playing in closed locations before (DC Metro, NYC Subway, etc) …

it’s not like you can miss the sound.That said, people heard it. The masses heard it. And it didn’t stop them in their tracks. But what if they’d been told in advance? Would they then stop and say, huh, so that’s beauty/art (just like a museum telling us)? Do we the common man require an elite few to tell us what is beautiful? Or if it was truly inherently beautiful, would people not have stopped on their own to admire it, awestruck?

## RE: Inherent Beauty or Explicit Beauty by scottb

I don’t think either of those really capture the issue.

Chaccone is a complicated piece, and solo violin pieces have a certain technical complexity to them as well. If you don’t understand that complexity, you’re probably not going to appreciate the piece — that’s even more likely if you’re not primed to be looking for it.

I think that when we apply the term “beautiful” to art, we mean something different than when we apply it to a woman (or man). In the latter case, we’re basically programmed by our genes to recognize the essential characteristics automatically. (Or, looked at another way, what defines those characteristics — what makes them essential — is that our genes program us to respond to them.)

With art, it’s a little different. Sure — you can look at some photographs and say, “that’s beautiful” — the subject might actually be a beautiful woman, or an environment that triggers emotional responses of comfort and safety. But not all of it falls in that category, nor should it.

Consider that we routinely talk about mathematics and software in aesthetic terms. Many (I’m one) consider

e+ 1 = 0 to be an inherently beautiful mathematical result. Pointing out that it contains each of the five most fundamental numbers in math (0, 1,^{iπ}e,i, andπ), exactly once each, along with exactly one addition, one multiplication, and one exponentiation, hints at why this is. But the more you know about what’s going on there — raising e to an imaginary power becomes a rotation about the origin, the connection with the Pythagorean theorem and trigonometry, and so on — the more beautiful it becomes.None of that beauty is accessible to someone without any mathematical background at all, who just sees marks on a page. Likewise, we shouldn’t expect someone without previous exposure to violin solos and classical music in general, without some basic technical knowledge to understand them, to appreciate Chaccone, regardless of the virtuosity in the performance.

We don’t need an “elite few” to tell us what’s beautiful — but we do need to understand what we’re seeing/hearing. It happens that in modern America, relatively few learn enough to understand and appreciate this particular performance.

The article did note that two people — both of whom had violin lessons as children, but neither of whom could by any stretch be identified as “musical elites”, but who did have enough knowledge to understand what they were hearing — did stop and stay for as long as they could. Not a lot, but it really just goes to show how small the portion of the public that can understand this particular content is.

## RE: Inherent Beauty or Explicit Beauty by Occams

I am sure that Brandon would feel the same about his head-banger music. You have to understand its context to appreciate it. You either get it or you don’t, and both positions are equally commendable.

Congratulations on E^in +1=0 . You stumped Wolfram Alpha. “1 = 0 FALSE”.

I am no mathematician, but I don’t understand how a complex number +1 can always equal 0 – because E^in will usually have an imaginary component and sometimes it will = 0 on its own.

I agree with your general observation about elites not owning what is beautiful.

I find many classical compositions beutiful, specifically: Most of Mozart; much of Beethoven; and, many by Bach. I love Flamenco and classical guitar, but I don’t like any pieces merely because they are complex or difficult to play. Sometimes a single instrument or quartet version of a theme will sound more beautiful than an a full orchestral performance (E.g LVB’s 9th Symphony, or the Largo from Dvorak’s New World. The music has to lift my spirit by somehow resonating with my mood at the time.

## Correction by Occams

That should of course be e rather than E in the equation above.

## RE: Correction by scottb

It should also be the greek letter pi, rather than n. Unfortunately, the sans-serif font that Omninerd uses makes ‘π’ look a lot like ‘n’.

The symbols in the equation are all constants.

‘e’is Euler’s number, the base of the natural logarithms,‘π’is the ratio of a circles circumference to its diameter,‘i’is the imaginary unit (the square root of -1), and ‘0’ and ‘1’ are the additive and multiplicative units (or the first two natural numbers, if that’s more familiar).## RE: Correction by scottb

Try it like this: e^(iπ) + 1 = 0

## RE: Inherent Beauty or Explicit Beauty by scottb

I am no mathematician, but I don’t understand how a complex number +1 can always equal 0 – because E^in will usually have an imaginary component and sometimes it will = 0 on its own.

Nope. A non-zero constant raised to a power can never be zero. If the exponent is zero, then

e= 1. Negative exponents result in positive fractions between 0 and 1, positive exponents result in numbers larger than 1.^{0}Here, though, we’re using an imaginary exponent, and (as I pointed out in another response) it’s not a variable

n, but the constantπin the exponent.Here’s a little more detail on how it all works out. First, the number

eis special because it represents a “fixed point” with respect to the operations of differentiation and integration. de^{x}/dx = e^{x}, and ∫e^{x}= e^{x}. That’s sort of the definition ofe— the specific constant that meets those constraints.But putting a specific value on

eis a little more complicated. One way of doing it is to form a Taylor series fromeand then substitute in 1 for^{x}x. The Taylor expansion is:1+x+x^2/2+x^3/6+x^4/24+x^5/120

If you notice the pattern, there, the denominators are the subsequent factorials. Someone who’s seen a lot of these Taylor series might remember seeing some similar patterns. It turns out that the Taylor series for cos(x) and sin(x) are very similar. In fact, it turns out that the series for cos(x) is exactly the even terms from

e, but with alternating signs, and the series for sin(x) is exactly the odd terms, again with alternating signs.^{x}If you plug in

ixforxin the expansions for all three, the signs line up perfectly, as each term gets a successively higher power ofi. So the end result of all this is we’ve discovered that:e= cos^{ix}x+isinxBut, if you think of that in terms of vectors in the complex plane, then what it’s saying is that

eis a unit vector that makes an angle^{ix}xwith the positive real axis. The cos(x) is horizontal, theisin(x) is vertical, theeis the hypotenuse of the triangle they form.^{ix}So now we see that

eraised to an imaginary power is a unit vector rotated to make an angle with the positive real axis equal to the real part of the exponent. But any number raised to an imaginary power can be rewritten to use e as the base instead, so it shows that imaginary powers represent rotation about the origin.So, now, instead of thinking of complex numbers as being

x+iy, basically a Cartesian coordinate system, we can think of them as beingre, a polar coordinate system. There’s lots of interesting chunks of analysis that derive from these observations.^{iθ}So, when you plug in π for the angle, then

e^iπ&is a unit vector rotated to make an angleπwith the positive real axis — in other words, it’s along the negative real axis, meaninge= -1, which (aside from putting the 1 on the other side of the equality) is the beautiful equation that started the whole thing.^{iπ}It’s amazing that we can take

ea transcendental number, raise it to an imaginary transcendental power, and yet end up not just close to -1, but dead on exactly there. And the various constants –e,π,i, 0, and 1, are so fundamental in mathematics, yet here they appear, once each, combined with such fundamental operations. Beautiful.## RE: Inherent Beauty or Explicit Beauty by Occams

Yes, as a radio engineer, I am familiar with the concept of the rotating vector because it is used frequently in the analysis of modulation systems, and for determining the phase relationships of rf waves.

I made my earlier comment when I thought that π was n, and that we were discussing an identity – true for all values of the variables, which would be much more interesting if true.

I agree that there is symmetry in the equation e^iπ +1 = 0 which could be described as beautiful to a mathematical mind for the reasons you state, but it really only reflects that for a particular angle , (*and presumably also for integer multiples of π), that e^iπ = -1

Infeed, π could be replaced by nπ in that equation making it even more beautiful, could it not?

## Correction RE: Inherent Beauty or Explicit Beauty by Occams

On reflectionn, I think e^iπn +1 = 0 only works when n is an even integer, and it may also have to be positive?

or e^(iπ2n) +1 = 0 where n is a integer

Is that more inherently beautiful, or too explicit?

## RE: Correction RE: Inherent Beauty or Explicit Beauty by scottb

I think it brings irrelevancies into it.

It actually only works when n is an odd integer. When n is an even integer, then

e– 1 = 0.^{iπn}As far as the aesthetics go, I think the original equation,

e+ 1 = 0 is the better one. To add more is a bit like explaining a joke — if you have to explain it, it’s not funny.^{iπ}To someone who understands

whythe equation is true, it brings to mind the connection between complex arithmetic and trigonometry, perhaps in the same way that music in a minor key tends to evoke emotions like melancholy. Adding in the extra variable would require carrying the caveat that n had to be an odd integer (or you could write it ase= ±1, with the caveat n ∈ ℤ). I think it loses some elegance.^{iπn}There’s also a certain purity in the original equation, which uses exactly one addition, one multiplication, and one exponentiation, together with one instance each of what are probably the five most important constants in mathematics. That’s why I prefer

e+ 1 = 0 to the equally true^{iπ}e= -1.^{iπ}## RE: Correction RE: Inherent Beauty or Explicit Beauty by Occams

It actually only works when n is an odd integer. When n is an even integer, then eiπn – 1 = 0.

You would think so because the cos and sin factors repeat every 2π, so Sin π is the same as Sin 3π, Sin 5π, etc. Same with Cos

But why then does Wolfram show it works with n=2 and n=4 but not for n=3?

## RE: Correction RE: Inherent Beauty or Explicit Beauty by scottb

You have to get the signs right. For odd n, the original formula,

e+ 1 = 0 works. For even n, you have to use^{niπ}e– 1 = 0.^{niπ}The value of sin(nπ) is always zero. The value of cos(nπ) is +1 for even n, -1 for odd n.

## RE: Correction RE: Inherent Beauty or Explicit Beauty by Occams

Agreed,

I think my motorcycle is a really beautiful thing but none of my family can see it.

## RE: Inherent Beauty or Explicit Beauty by Anonymous

regarding your e ^ (i * pi), when you raise e ^ (i * whatever), it is equiv to walking around the unit circle (like with sin and cos values), with the imaginary axis as the vertical axis, with a value equal to ‘whatever’ radian. so starting from 1,0 (1 + 0i), pi radians walks you 180 degrees to -1 + 0i.

## RE: Inherent Beauty or Explicit Beauty by Occams

I have no difficulty believing that if a random selection of Americans were put in an ideal concert hall and were exposed to this music, most of them would not like it very much.

It is really popular music from two centuries ago, and most of us don’t much like the popular music of the 1970s.

The question is really: is some music so inherently beautiful that most people will acknowledge that if exposed to it for the first time under ideal conditions? Now that would bew an interesting experiment.

I think that musical taste is a function of tase, experience fashion, educartion, and peer pressure. That is the basis for my initial statement here.