\magnification=\magstep1
\nopagenumbers
\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.

\bigskip
\noindent
{\it Specific Comments}
\bigskip
\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.
\vfill\eject
\noindent
{\it John Vatalaro -- Streaks and Statistics}
\bigskip
John, your paper on streaks and statistics is well-written and
you make your points strongly.  However, I think that
some of your reactions to Mlodinow's contentions were maybe
colored a bit too much by emotion (see comment 2).  I don't
see that Mlodinow was trying to say that DiMaggio's
streak is any {\it less admirable} just because similar
or longer streaks are actually somewhat likely on the
basis of probabilities.  I think he is just trying to
explain that it {\it may not be as exceptional} as we would like
to think it is.  It is also true that there are certainly questions
one could raise about the specific ways that the 10,000 simulations
of baseball were carried out.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I don't quite agree that this is what Mlodinow was saying.
I think it would be fairer to say that his point was that in any sport
(and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.  He would be the
first one to acknowledge that long streaks
of positive outcomes will happen {\it more often} for players who have a
high level of skill or dedication than for others -- their skill and
dedication makes it more likely that a good outcome happens
in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  Note that the simulated players who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game.
\item{2)}  I guess it is natural to react this way, especially
if you see the conclusion of this article as a threat to the
memory or reputation of a great player like DiMaggio.  However,
again I would say that this is not Mlodinow's real point.
I think the basic thing he is trying to get across is that
streaks are more common and longer than we tend to think
based on our limited understanding of probabilities.  I don't
think that takes anything away from DiMaggio, but it does
raise the question why his record has stood for so long(!)
And if you want to really argue the position you are taking
here, I think it would be good to try to come to a more
explicit explanation of exactly what it is about the full human
experience of playing a sport that makes a box model an
insufficient representation of the ``real thing.''  Here is one
example of a real issue I see -- it may very well
be the case that using a single life-time batting average in
a simulation like this ``smooths things out too much'' and ignores
the up and down variation in a player's performance over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more(!)
\vfill\eject
\noindent
{\it Brandon Nunn -- How likely are ``streaks'' in sports?}
\bigskip
This is a generally well-written essay on the points Mlodinow
raised in his article about streaks in general and DiMaggio's
streak in particular.  I sense that you may be ``of two minds''
about this, though, because the first three pages of what
you wrote seemed to be heading toward saying that the
simulation of 10,000 alternate baseball histories
by Arbesman and Strogatz  might
not have been realistic enough to justify the conclusion
that streaks like DiMaggio's are not that uncommon.
But then you spend the rest of the paper more or less
summarizing what Mlodinow said in {\it The Drunkard's
Walk} about some reasons why human perceptions are not
well developed for the estimation of probabilities.
The ultimate conclusion is good, but {\it the level of
mis-estimation} of probability involved in Arbesman and
Strogatz's model strikes me as much less than the crude
estimates of probabilities that humans make naively.  I guess
you are trying to say that even people using the mathematics
in a correct way can come to incorrect conclusions if they
don't capture all the relevant aspects of the real world in
their mathematical models.   It might have been better to make
this point even more explicitly.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I don't quite agree that this is what Mlodinow was saying.
I think it would be fairer to say that his point was something
you come around to saying later in the paper:  In any sport
(and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.  He would be the
first one to acknowledge that streaks
of positive outcomes will happen {\it more often} for players who have a
high level of skill or dedication than for others -- their skill and
dedication makes it more likely that a good outcome happens
in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  Note that the simulated players who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in multiple ways), he was certainly one of the all-time
greats in the game.
\item{2)}  You are raising some very good points here -- it may very well
be the case that using a single life-time batting average in
a simulation like this ``smooths things out too much'' and ignores
the up and down variation in a player's performance over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more(!)
\item{3)}  I think you could say the opposite, though.
Aren't those human qualities exactly what would lead a player
to accumulate a .325 lifetime average in the first place?  No
one who wasn't very talented, persistent, and extremely dedicated
could do this over a 15-year career.
\item{4)}  You are starting to overuse the superlatives like
``incredible'' at this point!  Ripken's consecutive game streak
strikes me as a very interesting combination of a very tough
mental attitude that allowed him to play through the minor aches
and pains all baseball players have,  plus {\it a lot of luck}
in that he never had a major (say season-ending) injury through
those years.  The times I saw him play, I certainly never got
the impression he was ``playing it safe'' or holding anything
back.  Maybe his body was more durable than average, but a lot
of this record has to be attributed to luck, I think.
\vfill\eject
\noindent
{\it Nick Foster -- Joe DiMaggio's Streak}
\bigskip
You argue your position (that probabilities are not the last
word in human activities like sports and that they should not be applied
to questions such as whether a streak like DiMaggio's is likely) quite
strongly and eloquently.  Your writing is also generally very good.  I'm
not sure I would go as far, though.  I would not totally
rule out the possibility of gaining insight about the outcome
of sporting events by using probability-based simulations like
the one by Arbesman and Strogatz that Mlodinow describes, even though,
as you point out, it is not entirely clear to what extent the results
of that simulation should be believed.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I don't quite agree that this is what Mlodinow was saying.
I think it would be fairer to say that his point was that in any sport
(and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.  He would be the
first one to acknowledge that long streaks
of positive outcomes will happen {\it more often} for players who have a
high level of skill or dedication than for others -- their skill and
dedication makes it more likely that a good outcome happens
in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  Note that the simulated players who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game.
\item{2)}  I agree that there are some questions one should
ask before accepting the results of this simulation of 10,000
histories of baseball.  For instance, did they really use
a single lifetime batting average for each player (effectively
treating each player like a robot)?  I think it is clear that
doing the simulation that way would ``smooth things out too much''
and ignore the up and down variation in a player's performance over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more(!)
\item{3)}  Likewise, I don't know the extent to which
Arbesman and Strogatz tried to take into account the
head-to-head matchups of batter versus pitcher in their
simulated histories.  I think that doing this in a realistic
way might address the objection your are raising here.
Programming a simulation with that level of detail
would be difficult, but I don't see that it would be
{\it impossible}(!)
\item{4)}  It is certainly true that the unlikely ``upset''
outcomes are the ones we remember the most and they are
a big part of why people follow sports.  But is it really
wrong to ask how unlikely a given feat really was?  It seems
to me that an informed understanding of exactly how likely
or unlikely some favorite sports record was is something a
true fan should {\it want to have}!
\item{5)}  Picky point -- these are not complete sentences.
You could say something like:  ``Consider the USA-Soviet
hockey game from the 1980 Olympics, ... ''
\vfill\eject
\noindent
{\it Carl Losito -- How Likely are ``Streaks'' in Sports?}
\bigskip
I agree that your position (that skill and dedication
have to count for something in sports) is intuitively
appealing.  But also see comment 7 below for one
possible response to this.  Of course, there are
also questions about the
way the simulations of 10,000 alternate histories
of baseball were carried out that would have
to be addressed in order for those conclusions to
carry the amount of weight that Mlodinow attributes
to them (see comment 5).  But I think you probably would agree
that this certainly thought-provoking!

I think your writing has improved over the year, but
there are still a number of places where your word choices
seem obscure to me.  The specific terms you use
are hard to understand because it is not obvious that
they fit with the rest of what you are saying.  I marked
a number of these in the paper, and see some of the
comments below as well.   Another
technical point is that in an extended discussion of
an article like the one you are doing here, it is
certainly OK (and it sounds somewhat more natural to me)
to use the {\it present tense} consistently -- say Mlodinow
introduces, concludes, describes, etc.  rather
than introduced, concluded, described, etc.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I don't quite understand what you are getting
at here.  To ``stifle'' someone usually means to keep
him or her from speaking or acting by exerting some type of
influence or force.  I can't see how that applies here.
\item{2)}  I think you mean something like ``can come about
through chance.''
\item{3)}  This is not quite correct.  Mlodinow reports the
results of the simulated 10,000 alternate histories of
baseball, but he did not carry out the simulations himself.
They were done by two mathematicians at Cornell, Arbesman and
Strogatz.  Be careful about attributions of credit like
this.
\item{4)}  Again, I don't quite understand what you are
getting at here.  How does denying the influence of randomness
``maintain stability?''
\item{5)}  I agree that there are some questions one should
ask before accepting the results of this simulation of 10,000
histories of baseball completely.  For instance, did Arbesman and
Strogatz really use
a single lifetime batting average for each player (effectively
treating each player like a perfectly consistent robot)?  I think it is clear that
doing the simulation that way would ``smooth things out too much''
and ignore the up and down variation in a player's performance from
day to day over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more(!)
\item{6)}  I don't quite agree that this is what Mlodinow was saying.
I think it would be fairer to say that his point was that in any sport
(and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.  So the {\it likelihood}
that someone would have had a similar streak is high.  It is not
possible to say with certainty that someone else would have done
it.
\item{7)}  I think it is important to understand that
Mlodinow would definitely be the
first one to acknowledge that long streaks
of positive outcomes will happen {\it more often} for players who have a
high level of skill or dedication than for others -- their skill and
dedication makes it more likely that a good outcome happens
in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  Note that the simulated players who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game.

\vfill\eject
\noindent
{\it Josh Hauser -- Streaks}
\bigskip
You raise some good points in your essay about Mlodinow's
article on DiMaggio's 56-game consecutive hitting streak.
But I don't think your ideas carry the weight they could
because of the way they are presented.
See the comments below and some corrections marked on the
paper for some suggestions on issues related to the writing.
In general, I would say that you are using a somewhat
too informal style here.    Phrases like ``ridiculous season''
are fine in everyday speech, but you should try to find
less colloquial equivalents for formal writing.  Also,
in referring to the author of a book or article you
are discussing, you should always use the person's last
name (i.e. ``Mlodinow'') not the person's first name
(i.e. ``Leonard'').  You are not on a first-name basis
with him here, so to speak(!)
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  You should say here that the simulation you
are referring to was conducted by two mathematicians
at Cornell (Arbesman and Strogatz).
\item{2)}  I think everyone would agree that there was
{\it some} luck or randomness involved in DiMaggio's
streak.  To say otherwise is to say, in effect, that
he could control every aspect of the games he played
in.  If that was true, why did the streak end?
The real issue is how likely it was for anyone to
have a consecutive game hit streak that long or longer.
\item{3)}  It would be a nice exercise to try to
see where this $75\%$ chance figure came from.  Think
about the binomial probabilities for getting at least
one hit in 4 at bats, if you use DiMaggio's lifetime
average of .325 as the probability of getting a
hit in any one at-bat.
\item{4)}  I don't think that is quite what the
article says.  The point is that people tend to think
of ``hot'' or ``cold'' streaks as coming from some
change in the athlete.  Saying you are ``in the zone,''
for instance seems to say that you have found some
particularly productive mental state to be in, and
that is what is {\it causing} the better than average
outcome.  But what the article is arguing is that
the same kind of hot or cold streaks would be
observed if there were no changes in the athlete,
just normal random variation in the outcomes.
\item{5)}  You are raising a very good point here -- it may very well
be the case that using a single life-time batting average in
a simulation like this ``smooths things out too much'' and ignores
the up and down variation in a player's performance over a game or
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more(!)
\item{6)}  This is another very good point.  I think this
says that in effect the Yankees' opponents {\it did not}
make any special attempt to shorten the streak -- they
may have thought that, out of a spirit of good sportsmanship
or whatever, they should give DiMaggio a chance to keep
the streak going if he could.
\item{7)}  Careful -- these factors are not ``confounders''
in the precise sense we used that term in the first semester.
They are not factors associated with the treatment and the
outcome of a study.
\item{8)}  You seem to be arguing against your own point
here.  With 30 teams, there are many more
players active in the major leagues than there were
when DiMaggio was playing (and there were only 16 teams).
This should make it more likely that a long
hitting streak would happen {\it now}.
\item{9)}  I don't know about this either.  You could certainly
argue, though, that with the increased specialization of
starters with strict pitch count limits, set-up men, eighth-inning pitchers, and closers,
batters are facing consistently {\it fresher} pitching.
\vfill\eject
\noindent
{\it Patrick Jarvis -- How likely are streaks?}
\bigskip
This is a good essay about Mlodinow's discussion of streaks in
baseball, although there are some places where I think you
are misrepresenting what Mlodinow was saying--it is a bit
more ``nuanced'' than you are acknowledging.  It was
good that you tried to explain some of the probability
calculations.  But there was one small thing that you
overlooked.  See comment 5 below for the correct way
to estimate the probability that a weaker team will win
a $7$-game World Series in the particular case you
were looking at.

See the paper for some (relatively minor) suggestions
for rewording or rephrasing some things.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I don't quite agree that this is what Mlodinow was saying.
I think it would be fairer to say that his point was that in any sport
(and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.
\item{2)}  Mlodinow would be the
first one to acknowledge that long streaks
of positive outcomes will happen {\it more often} for players who have a
high level of skill or dedication than for others -- their skill and
dedication makes it more likely that a good outcome happens
in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  Note that the simulated players who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game.
\item{3)}  I don't understand what you are trying to get at here.
The issue is not really ``accuracy of results.''  It is how likely
the ``outliers'' are.
\item{4)}  This figure depends on the probabilities that each
team wins in a single game -- the $40\%$ is based on the $55\% - 45\%$
probabilities.
\item{5)}  This is a good try, but you are not thinking about how
to compute the probabilities in exactly the right way.  The chance
of an event
{\it cannot} come out to be greater than $100\%$.  The reason one
of yours did was that you were counting the same outcome
multiple times.   Here is the way you
need to do it:  If the weaker term wins in four games, then
the binomial probability formula gives $(.45)^4$ (about 4\%) as you say.
If they win in $5$ games, then the thing you were not seeing is that
they have to {\it win the fifth game}, so
the binomial probabilities only apply to {\it the first four games}:
${4\choose 3} (.45)^3 (.55) (.45)$ (where the last $.45$ represents
the fifth game).  There is about a $9\%$ chance of this.  Similarly, the probability that they win in
six games is ${5\choose 3} (.45)^3 (.55)^2 (.45)$ (about a $12.4\%$ chance), and the
probability that they win in seven games is ${6\choose 3} (.45)^3 (.55)^3 (.45)$
(about a $13.6\%$ chance).  The {\it sum} of these is $4 + 9 + 12.6 + 13.4 \doteq 39\%$
(a bit more, since I rounded down).  This is where the ``about $40\%$'' figure comes from.
\item{6)} ``Recreated 10,000'' times is not the best way to describe what
happens in simulations like this.  What the program did was to
run through a simulation of the history of baseball 10,000 times, but
with different outcomes based on random factors determining the outcome
of at-bats, games, etc.
\item{7)}   Careful -- these factors are not ``confounders''
in the precise sense we used that term in the first semester.
They are not factors associated with the treatment and the
outcome of a study.
\item{8)}  I do not see that this is relevant.  The issue is
how often we should expect a professional baseball player
to have a streak like DiMaggio's.  What average people could
do is not the point.
\item{9)}  Again, I don't think this is what the program
that Arbesman and Strogatz wrote was trying to do.  They
were'nt trying to {\it predict} outcomes, just explore
the range of different outcomes that were probable enough
to show up in the 10,000 simulated histories of the game.
\item{10)}  You are raising a very good point here -- it may very well
be the case that using a single life-time batting average in
a simulation like this ``smooths things out too much'' and ignores
the up and down variation in a player's performance over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more about exactly
what they did(!)  In other words, while their results are
suggestive, I would not want to accept their claims uncritically
without more precise information about exactly what they
did!
\item{11)}  It is interesting that you are trying to argue
this way, because it seems to me that you could
make exactly the same criticism of someone who
says that DiMaggio's streak could only have come about
because of the exceptional talent and dedication of
a great player.  This is the main point of Mlodinow's
article and the Arbesman-Strogatz simulation study
too.  We underestimate the potential for long streaks
just based on chance because we want to believe that
humans have ultimate control over the events in their lives.
\vfill\eject
\noindent
{\it Greg Monfette -- Streaks in Sports}
\bigskip
Good essay on the Mlodinow article about the role of streaks
in sports.  You have brought in some good additional examples
and your writing is very strong here.  I have marked some
minor suggestions on the paper itself, but overall I think
this is probably your best writing so for our class(!)
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}   I don't quite agree that this is what Mlodinow was saying.
I think it would be fairer to say that his point was that in any sport
(and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.
\item{2)}  As you indicate, Mlodinow would be the
first one to acknowledge that long streaks
of positive outcomes will happen {\it more often} for players who have a
high level of skill or dedication than for others -- their skill and
dedication makes it more likely that a good outcome happens
in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  Note that the simulated players who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game.
\item{3)}  Instead of saying ``world/dimension'' here, it might be
better to say ``simulated history.''
\item{4)}  You are raising a very good point here -- it may very well
be the case that using a single life-time batting average in
a simulation like this ``smooths things out too much'' and ignores
the up and down variation in a player's performance over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly.
I think it would be very interesting to learn more about exactly
what they did(!)  In other words, while their results are
suggestive, I would not want to accept their claims uncritically
without more precise information about exactly what they
did!
\item{5)}  ``A better life'' sounds somewhat ``wishy-washy.''
You are saying something much more specific, namely that
an understanding of the role of chance would give people
a more realistic view of the things that happen in their
lives.
\vfill\eject
\noindent
{\it Jack Karlovec -- Streaks in Sports}
\bigskip
You take a pretty strong position here that probabilities
basically don't have much to say about outcomes
of sporting events and the likelihood of streaks like
DiMaggio's.  I agree that this position is intuitively
appealing.  Your writing is also very good for the
most part -- certainly the best writing I have seen
from you all year.

However, there is a major aspect of the Mlodinow article that
you have not mentioned at all -- the results of the simulation
of 10,000 alternate histories of baseball by the Cornell
mathematicians Arbesman and Strogatz.  It seems to me that
that deserves some mention, because it would be possible
to argue (as Mlodinow does) that those results show the
exact opposite of what you are claiming.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I think you are misrepresenting Mlodinow's
point here by saying the alternative is ``streaks
are simply flukes.''  I think it would be fairer to say that his point was
that in any sport (and even more generally in many areas of life), streaks of positive
or negative outcomes {\it can happen}, due to chance, more often than
our human perceptions are geared to understand.  Mlodinow would be the
first one to acknowledge that long streaks of positive outcomes will happen
{\it more often} for players who have a high level of skill or dedication
than for others -- their skill and dedication makes it more likely that a good
outcome happens in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  I think it is very telling that the players
(in the computer simulations you did not mention) who
beat DiMaggio's record the most often were not ``slouches;'' they
were other acknowledged major stars like Ty Cobb(!)  Whatever
you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game, with a level of skill and dedication
similar to DiMaggio's.
\item{2)}    I don't think that the ``hot hand'' in basketball
is something that everyone would agree about.
Mlodinow, in fact, would say there is no such thing.
His point is that people tend to think
of ``hot'' or ``cold'' streaks as coming from some
change in the athlete.  Saying you are ``in the zone,''
for instance, seems to say that you have found some
particularly productive mental state to be in, and
that is what is {\it causing} the better than average
outcome.  But what the article is arguing is that
the same kind of hot or cold streaks would be
observed if there were no changes in the athlete,
just normal random variation in the outcomes due to
chance and probability.
\item{3)}  Bringing up all the circumstances and events that
can influence the outcome of baseball games is not a
very strong argument against Mlodinow's position, in my
opinion.  The reason is that someone who wanted to take
the opposite position could just say that all those
circumstances are exactly what goes into determining
the statistics of players.  And it is those career
statistics that were used by Arbesman and Strogatz to predict
that long hitting streaks should happen relatively
more frequently than we want to believe.
A much stronger question to raise would concern
the way those simulations were done.  For instance,
it is not very clear from what Mlodinow wrote whether
a batter's {\it lifetime average} was used to estimate
the probability of outcomes in every simulated at-bat.
As you can probably tell, it may very well
be the case that using a single life-time batting average in
a simulation like this ``smooths things out too much'' and ignores
the up and down variation in a player's performance from day to day over
a single season.  Running into a local cold stretch over a couple
of games could easily ``kill'' a hitting streak.  Similarly,
it is not clear whether the simulation took specific pitcher-batter
matchups into account.   I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
these criticisms and designed their computer program accordingly.
I think it would be very interesting to learn more about exactly
what they did(!)  In other words, while their results are
suggestive, I would not want to accept their claims uncritically
without more precise information about exactly what they
did!
\vfill\eject
\noindent
{\it Mary Arnold -- Streaks in Sports}
\bigskip
This is an excellent summary of the Mlodinow's article on
the DiMaggio streak and related topics from {\it The Drunkard's
Walk}.  You were actually the only one who wrote on this
topic to more or less acknowledge the possibility that
chance could have had a big role in a streak like DiMaggio's
famous example.  Everyone else really wanted to hold
to the idea that {\it only} the human factors you mention should
be taken into account!  Everyone else seemed to think
that saying chance played a role was somehow diminishing
DiMaggio's accomplishment.  But of course, Mlodinow would be the
first one to acknowledge that long streaks of positive outcomes will happen
{\it more often} for players who have a high level of skill or dedication
than for others -- their skill and dedication makes it more likely that a good
outcome happens in {\it every at-bat}, so it is also more likely that they
have longer hot streaks.  I think it is very telling that the players in the
computer simulations who beat DiMaggio's record the most often were
not ``slouches;'' they were other acknowledged major stars like Ty Cobb(!)
Whatever you think of Cobb as a person (he was apparently a really unpleasant
character in several ways), he was certainly one of the all-time
greats in the game, with a level of skill and dedication
similar to DiMaggio's.


Your writing is very good -- I had
only a few suggestions for changes.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  When you say it this way, the probabilities of streaks
do sound more likely.  There is a point here, though, that
should not be passed over too lightly.  It may very well
be the case that using a single life-time batting average in
a simulation like this ``tends to smooth things out too much'' and ignores
the inevitable up and down variation in a player's performance over a game or
a single season.  This is especially true for the specific situation
of the consecutive game hitting streak because one ``off day'' could
easily ``kill'' a hitting streak.  I have not looked into
the details of how Arbesman and Strogatz carried out their
simulation enough to be able to say whether they anticipated
this criticism and designed their computer program accordingly
(perhaps by allowing some random up and down variation in
the simulated players' averages over a simulated season).
I think it would be very interesting to learn more(!)
\item{2)}  I think there is also an element of psychology
here.  To a player in the middle of a hot streak, there
can be a perception of being invincible, or ``in a zone,''
or having a ``hot hand.''   To them, it feels as though there
is something different about them at that time, or that they
are doing something different {\it to make the streak happen}.
I think this is another aspect of our human tendency to look
for reasons and explanations of things in our experience.
\item{3)}  See the general comments above.  If you admit
that streaks are more likely than we sometimes think
because of chance, then it is perhaps
not surprising that DiMaggio was the player to
have the longest streak in the actual history of
the game, because of his high level of talent and
consistency.
\vfill\eject
\noindent
{\it Paige Carr -- Human Misperception of Randomness}
\bigskip
This is a good summary of the discussion of why humans tend to misperceive
the effects of randomness, along the lines of our class discussions and
{\it The Drunkard's Walk}.  But this paper was supposed to be 
somewhat more specific about the probability of long
consecutive gave hitting streaks in baseball along the
lines of DiMaggio's famous record streak.  

Unfortunately, you have not discussed
one of the most interesting aspects of the Mlodinow article from
the Wall Street Journal
about DiMaggio's streak at all. I think this means that
you have not really addressed some of the interesting features
of this particular baseball record, and a key piece of evidence
of how likely long hitting streaks might be.  
I am referring to the computer simulation of 10,000 alternate 
histories of baseball by the two mathematicians Arbesman and 
Strogatz at Cornell using the actual players' statistics for each 
year to estimate probabilities for different occurrences.  Although
I think there are questions one could ask about the methods
they used, I think their results seem to be {\it quite convincing}
about the likelihood of long hitting streaks -- in 42\%
of the ``parallel histories,'' in fact, there were streaks
as long or longer than DiMaggio's actual record streak.  

Of course as you mention at one point, the skill and dedication
of players matter too for this, and in fact it was usually 
some of the best players in history (for example, Ty Cobb) who were the ones who
had the long simulated hitting streaks.

Your writing is very good here -- there were hardly any changes I 
found to suggest.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  In this case, it would still be the case that the
expected number of heads or tails would be half the
total number of tosses.  The complicated psychological
thing about this example, I think, is that long ``streaks''
of heads or tails {\it don't seem random to us}, even though
the probabilities tell us that they can happen.
\item{2)}  What chance are you thinking of here?  I think
this refers to the chance that DiMaggio would get
at least one hit every 4 at-bats (a typical number
for a 9-inning game).  
\item{3)}  This is not quite correct.  The Kahneman-Tversky
article you are referring to is actually called ``The Hot Hand
in Basketball.''   The point they were trying to make
was that people tend to think
of ``hot'' or ``cold'' streaks (such as long consecutive
strings of hitting free throws or 20-foot jump shots)
as coming from some particular state in the athlete at
the time.  Saying you are ``in the zone,''
for instance, seems to say that you have found some
particularly productive mental state to be in, and
that is what is {\it causing} the better than average
outcome.  But what the article is arguing is that
the same kind of hot or cold streaks would be
observed if there were no changes in the athlete,
just normal random variation in the outcomes due to
chance and probability.
\item{4)}  Even without bringing in the influence
of a higher power, there is the issue of perception
mentioned above (see point 3.)


\bye
