Amanda Cabrera – (no title)

Your essay about issues of authenticity and chance in music and other art forms is mostly very good! You raise some interesting issues and introduce one superb example (the Carlos Santana performance from the 2005 Academy Awards show).

I have marked a number of relatively small corrections on the paper itself. Almost all of these are issues of word choice, or of getting a phrase exactly right. Your writing is generally good, but there are enough of these here that I would say this is something you should think about. I find it often helps to try reading something I am writing out loud (perhaps to another person). Awkwardnesses really show up when you do that.

Specific Comments

1) This is a great example and it shows that at least some composers have such a personal attachment to the music they create that they resist having other musicians reinterpret what they have done. As you go on to say, of course, not all composers think this way though.

2) This raises a couple of very interesting points. First, to what extent did the composer actually have a specific instrument in mind in composing the piece? There are examples both ways, of course. A lot of classical music is very specific about what instruments should be used because the specific quality of the sound the instruments make is part of what the composer had in mind. (Think of the difference between a melody played on a flute and the same melody played on a trumpet!) But there are other examples (such as some pieces that J.S.Bach wrote toward the end of his life) where there are no indications at all what instruments should be used. It almost seems as though what he wrote is “pure music” that could be (and has been) performed on almost any combination of instruments that could produce the notes. Second, to what extent was the composer actually satisfied with what might have been available at the time the music was composed? There are some very well-documented cases where a composer was very dissatisfied with the sound quality of the instruments that were available to him. Beethoven, for example, constantly complained about the weaknesses of the pianos that were available in the early 1800’s, and destroyed several pianos he owned out of frustration (even before his deafness!). It seems very likely he would have jumped at the chance to have his music performed on a modern grand piano – it would have been closer to the “ideal instrument” he heard in his mind’s ear.

3) It is also interesting to realize that, at the time much “classical music” was written, it was essentially the popular music of the time. The fact that it has survived so long creates whole new layers of questions about authenticity and interpretation. I doubt that many composers from the second half of the 18th century (other than Mozart and Haydn, perhaps) would have expected that their music would still be performed over 200 years later!

Steph Craig – The Underlying Meanings of Music

Good job on this assignment. Your writing is really strong, and you raise some interesting points. However, I think one of your basic working assumptions is somewhat questionable (even though it is certainly intuitively appealing). See comment 1 below for this.

Specific Comments

1) The sentence I marked here does not seem to follow what you said before. I thought you were going to say “It is possible however that these messages are not the ones that listeners perceive.” And this whole paragraph raises an interesting and important point about music. Namely, I agree that when you are listening to a piece of music, it can certainly seem that some sort of information, or emotional state, or story is being conveyed. But if you try to pin down exactly what that is, it is surprisingly hard. Moreover, it is never clear that different listeners will “get” the same thing from a given piece of music if they are presented the music “cold,” that is, without any accompanying verbal explanations or cultural associations. Many philosophicallyinclined musicians who have tried to think about these questions have come eventually to the point of view that there is no underlying meaning in music at all – just patterns of sound that provoke different responses in different listeners. (You actually come around to saying something like this on page 4.) That is somewhat unsatisfying, but if you want to argue that there is meaning in the music itself, then as I said before, it is hard to specify exactly what it is!

2) By “their attempts are justified,” I think you are trying to say something more like “they can try to control the perception of their music if they want (by specifying how it should be performed).” But as you say next, this kind of attempt is essentially doomed to fail because performers will do their own thing anyway, and individual listeners will always interpret the music they hear on their own terms. I more or less agree with what you are saying here as a practical matter. Your “everything’s OK” position is a demonstration of what I was saying above about the difficulty of identifying exactly what is conveyed by music, though.

3) I think another aspect of the “tortured feeling” you bring up here is that it is often extremely difficult for composers (or writers, or artists, ... ) to realize their artistic vision in their chosen medium. Having a great idea for a piece of music is the first step, but actually getting it down on paper, and then having it performed require struggles that can often “eat at a composer’s soul,” as you say.

Dan Schmader – Artists, Choices, and Chance

This is a good paper on some of the issues about authenticity, originality, etc. in performance of music. You have some interesting and different viewpoints about some things and you have expressed them well for the most part. The major criticism I have about your writing here is that the organization into paragraphs is not always very clear. Paragraphs seem to run on very often even though you are introducing new ideas or changing topics. The conclusion is also a bit weak because the last paragraph repeats many points you made before without developing them.

1) This is certainly true. Being remembered and having one’s music played, even if it is played in different ways than one expected in one’s lifetime, would certainly be preferable to a composer than being forgotten entirely!

2) This is an interesting idea – if I understand you, you are saying that by bringing their own knowledge of the modern instruments into play, Carol and Mark were adding something of themselves (or their own time) to the music and were more original than when they were playing the baroque instruments because of that. I never thought of it this way, but you might have a point, if you are thinking of the personal contribution of the performers when a piece of music is played and heard.

3) I do not know what you were getting at here. What did you mean when you said that Beethoven was gaining authenticity? (Also, you have a very long paragraph here that addresses a number of different, and not too closely related points. It should be divided into several smaller paragraphs, for instance by starting a new paragraph where I marked.)

4) You are right that Mozart contributed a great deal to the evolution of music over his lifetime. In addition to the example you give, it was also true that he was a leader in providing more prominent and more interesting and idiomatic music for woodwind instruments (clarinet, oboe, bassoon, French horn especially, flute to a lesser extent).

5) I know exactly what you mean here about the unexpected or unplanned things that can happen in musical performances. But I don’t think these chance occurrences are necessarily a case of “error.” The might be different from what the composer put down in the score, but they are not strictly wrong! Also, I don’t think your example the way Mark Kroll tried to get the audience to be really quiet or the way the lighting was set up in the room are really good examples of allowing for chance occurences. (It seems to me that, if anything, they are exactly the opposite – attempts to minimize the effects of randomness by getting the audience to be really still and to focus their attention on the stage area!)

6) Your last paragraph is another very long one, and it is mostly a “rehash” of ideas you had brought up earlier. A strong conclusion adds a lot to a paper (and a paper slightly shorter than 5 full pages would be OK provided that the conclusion really brought things to strong close!)

Shelby Proft – Artists, Choices, and Chance

I am not sure I agree with what you are saying about randomness in music, though the difference is one of degree, perhaps. I would say music performance is a mixture of random and deterministic elements instead of being “completely random.” Nevertheless you have used a good example and you have some interesting points.

I think you are also making good progress on the writing front. This paper is much clearer and more understandable than your work early last semester. There are still a few places where some rewording would help. But in general, this is good work!

Specific Comments

1) I don’t quite see how the differences in the sounds of the harpsichord and the modern piano are really a product of randomness. The piano was invented by an 18th century instrument maker who was trying to provide an instrument that could do different things than a harpsichord could. That is, pianos were designed to play loudly and softly depending on how the keys were struck, and also to be capable of sustaining sounds for a longer time than the harpsichord could. This was all very intentional, not random.

2) The human voice is the original musical instrument (for humans anyway!) and the ideal toward which almost all instruments strive. (For example, we say that other instruments can “sing” if they are played skillfully enough.) Also, you might be interested to know that I have read that the use of auto-tuning actually started out as a way to correct spontaneous mistakes in pitch made by singers and make their live performances sound more like their recordings. (To me this seems to be hardly different from lip-synching.) On the other hand, there are apparently some singers who make it a point not to use the auto-tuning machines for that purpose, because they think their authentic voices, with their small imperfections, are more expressive. So this kind of technology can cut both ways.

3) This is possible, but there are also some pieces that J.S.Bach wrote toward the end of his life where no indications at all are given what instruments should be used. It seems as though what he wrote was “pure music” that could be (and has been) performed on almost any combination of instruments that could produce the notes.

4) Again, I’m not sure if I agree with what you are saying here about the “completely random” nature of music – this seems too strong and too sweeping a statement. As you say, the performance of music certainly contains random elements. But there are nonrandom aspects too if the performers are trying to reproduce the music described by the instructions in a musical score.

5) It took me a while to figure out what you meant to say here, but I think this is an interesting point. If I understand what you meant by “continual,” it is that there would only be one completely authentic performance that would be repeated over and over with no changes. That would be boring!

Jonathan Ye – Does Randomness Exist?

This is a very well-written and entertaining essay. You have made (quite slyly and indirectly, but very effectively) an interesting point about the connection between apparent randomness and the information we have available. Things often look random because we don’t have complete information about them, and on the other hand things can be said to be random if they have a high degree of complexity or information content (see comment 1 below).

The only real criticism I have is that you might have included a somewhat fuller and more mathematical explanation of chaos in dynamical systems – see comment 2 below. Also, you are right that radioactive decay is an example of a physical process that is considered to be truly random (according to a standard interpretation of quantum mechanics). Of course, it is also possible to ask whether it even makes sense to consider an algorithm that would predict the decay of an atom of a radioactive isotope of some element like U^{235}! Is there anything that says such an algorithm must exist? In other words, how good is the proposed idea of randomness that you describe?

Specific Comments

1) I assume this is the MIT student Qiaochu Yuan whose blog I found via Google(!) You might be interested to know that this proposed definition of randomness is a version of an idea called the Kolmogorov complexity. In theoretical computer science, the Kolmogorov complexity of a string is the length of the shortest program that generates that string (where the program is in some universal language powerful enough to specify any algorithm). High complexity means that the shortest program that generates the string is comparable in length to the string itself. For instance the string “ababab ⋯ ab” with two million alternating copies of the characters “a”, “b” has very low complexity since a program to generate it could say, in effect, “repeat “ab” one million times,” and this is far shorter than 2 million characters long(!) This is one way to understand the fact that the string is not random. On the other hand, there might not be any way to generate a “really random” string shorter than just listing all the characters that make up the full string. This seems like a reasonable intuitive operational definition of randomness to me, at least in certain domains. For instance, it might be more applicable to abstract mathematical objects than to physical processes like radioactive decay(!)

2) Not exactly. Chaos theory is really the mathematical discipline that studies these phenomena. And a situation as simple as a dart in free fall is not one where “chaotic behavior” would be expected. In a chaotic dynamical system, such as the Lorentz system of differential equations, in principle, a trajectory is uniquely determined given the initial conditions. However, because of the sensitive dependence on the initial conditions, it is necessary to know the initial conditions exactly in order to make predictions about the long-term behavior of the trajectory. The initial values we need to know are represented mathematically as real numbers with infinite and nonrepeating decimal expansions. We can only make measurements to some finite precision (some finite number of decimal places). So even though the system is deterministic in principle, prediction is not possible because of the fact that we will never know the initial conditions exactly.

3) Pedantic comment – togas were worn in ancient Rome, not Greece. Although some ancient Greeks wore something similar, they were called by a different name(!)

Kyle Walraven – On Chaos and Randomness

This is an excellent and very well-written essay on a very subtle topic. I think you have the makings of a philosopher(!)

The only major critical comment I have is that your proposed definition of randomness has some deficiencies. (But don’t feel bad because this is an area where philosophers, mathematicians, and scientists have yet to come to complete agreement!) See comment 1 below for a first objection. And see comment 2 for an example that shows you need to be careful about the idea of “unpredictability” too. Does this mean “unpredictability in practice” or “unpredictability in principle?” There’s a difference, and there are deterministic (i.e. non-random) systems that are also unpredictable in practice.

You are right to point out that things often look random because we don’t have complete information about them. On the other hand it is interesting to note that one provisional definition of randomness (different from the idea you were trying to get across) is that randomness is essentially the same thing as a high degree of complexity or “information content.” There is another proposed definition of randomness coming from what is called the Kolmogorov complexity in theoretical computer science. The Kolmogorov complexity of a string is the length of the shortest program that generates that string (where the program is in some universal language powerful enough to specify any algorithm). High complexity means that the shortest program that generates the string is comparable in length to the string itself. For instance the string “ababab ⋯ ab” with two million alternating copies of the characters “a”, “b” has very low complexity since a program to generate it could say, in effect, “repeat “ab” one million times,” and this is far shorter than 2 million characters long(!) This is one way to understand the fact that this string is clearly not random. On the other hand, there might not be any way to generate a “really random” string shorter than just listing all the characters that make up the full string. This seems like a reasonable intuitive operational definition of randomness to me, at least in certain domains. But for instance, it might be more applicable to abstract mathematical objects than to physical processes like radioactive decay(!)

Specific Comments

1) This seems to be much too strong a requirement to me. A strict scientific materialist (one who believes that there is nothing else besides matter and equivalent energy in the universe – no “spirit” or consciousness independent of physical processes in matter) would argue that everything has to be governed by natural laws. It seems to me that your other ideas should be consistent with that position, so you don’t want to rule out that possibility with how you define randomness. Moreover, there are physical theories (such as a standard interpretation of the theory of quantum mechanics that describes matter on the atomic and subatomic level) where randomness is “built-in” in a certain sense. In fact, certain physical processes described by quantum mechanics, such as radioactive decay are usually considered to be purely random. Of course, like all scientific theories, quantum mechanics is just the best description we know at present of those physical phenomena, and it could turn out that in the future a different understanding, eliminating the randomness, will be achieved(!)

2) There is a fairly subtle point that could be better explained here. In a chaotic dynamical system, such as the Lorentz system of differential equations in meteorology (where the “butterfly effect” was discovered), in principle, a trajectory is uniquely determined given the initial conditions. So in mathematical terms, the system is strictly deterministic(!) However, because of the sensitive dependence of the trajectory on the initial conditions (and the strong mixing properties of the Lorentz system), it is necessary to know the initial conditions exactly in order to make predictions about the long-term behavior of the trajectory. But the initial values we need to know are represented mathematically as real numbers with potentially infinite nonrepeating decimal expansions, and we can only make measurements to some finite precision (some finite number of decimal places). So even though the system is deterministic in principle, prediction is not possible because of the fact that we will never know the initial conditions exactly. In other words, it is possible for a system to be predictable in principle, but unpredictable in practice.