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\noindent
{\it Amanda Cabrera -- (no title)}
\bigskip
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 {\it 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.    

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\noindent
{\it Specific Comments}
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\item{1)}  This is a {\it 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.  
\item{2)}  This raises a couple of very interesting points.
First, to what extent did the composer {\it actually have} 
a specific instrument in mind in composing the piece?
There are examples both ways, of course.  A lot of 
classical music is {\it 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.  
\item{3)}  It is also interesting to realize that, 
at the time much ``classical music'' was written,
it {\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!
\vfill\eject
\noindent
{\it Steph Craig -- The Underlying Meanings of Music}
\bigskip
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.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{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
{\it 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 philosophically-inclined musicians 
who have tried to think about these questions have come eventually 
to the point of view that there is {\it 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!
\item{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.  
\item{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 {\it 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.
\vfill\eject
\noindent
{\it Dan Schmader -- Artists, Choices, and Chance}
\bigskip
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.  
\bigskip
\item{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!
\item{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.
\item{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.)
\item{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).   
\item{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 {\it minimize} the effects
of randomness by getting the audience to be really
still and to focus their attention on
the stage area!)  
\item{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!)
\vfill\eject
\noindent
{\it Shelby Proft -- Artists, Choices, and Chance}
\bigskip
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!
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I don't quite see how the differences in the sounds
of the harpsichord and the modern piano are really a 
product of {\it 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 {\it 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 {\it intentional},
not random.  
\item{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 {\it not} to use the auto-tuning machines for 
that purpose, because they think their {\it authentic} voices, 
with their small imperfections, are more expressive.  So this kind
of technology can cut both ways.    
\item{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.
\item{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.
\item{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 {\it would be} boring! 
\vfill\eject
\noindent
{\it Jonathan Ye -- Does Randomness Exist?} 
\bigskip
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?     
\bigskip
\noindent
{\it Specific Comments}
\bigskip 
\item{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 {\it 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 $``ababab\cdots ab"$ with two million 
alternating copies of the characters $``a",``b"$ has 
{\it 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(!)  
\item{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 {\it 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 {\it exactly}.  
\item{3)}  Pedantic comment -- {\it togas} were worn in ancient
Rome, not Greece.  Although some ancient Greeks wore
something similar, they were called by a different name(!)
\vfill\eject
\noindent   
{\it Kyle Walraven -- On Chaos and Randomness}
\bigskip
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 {\it 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 $``ababab\cdots ab"$ with two million 
alternating copies of the characters $``a",``b"$ has 
{\it 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(!)  

\bigskip
\noindent
{\it Specific Comments}
\bigskip 
\item{1)}  This seems to be much too strong a requirement 
to me.  A strict scientific {\it 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 {\it 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 {\it 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(!)   
\item{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 {\it 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 {\it exactly}.  
In other words, it is possible for a system to be predictable
in principle, but unpredictable in practice.  
\bye
