\documentclass[%
version=last,%
a5paper,
10pt,%
headings=small,%
bibliography=totoc,%
twoside,%
reqno,%
cleardoublepage=empty,%
parskip=half,%
draft=true,%
%DIV=classic,%
DIV=12,%
headinclude=false,%
pagesize]
{scrartcl}

%\usepackage[notcite,notref]{showkeys}

\usepackage[polutonikogreek,english]{babel}

\usepackage[neverdecrease]{paralist}
\usepackage{hfoldsty,url,verbatim,relsize}

\usepackage{relsize} % Here \smaller scales by 1/1.2; \relscale{X} scales by X
\renewenvironment{quote}{\begin{list}{}
{\relscale{.90}\setlength{\leftmargin}{0.05\textwidth}
\setlength{\rightmargin}{\leftmargin}}
\item[]}
{\end{list}}

\usepackage{verse}

\usepackage{pstricks,pst-node,pst-tree}
\usepackage[all]{xy}
%\usepackage{auto-pst-pdf} % This is so that pdflatex works; but then one must run pdflatex -shell-escape (or pdflatex --enable-write18 in MikTeX).  See  http://tug.org/PSTricks/main.cgi?file=pdf/pdfoutput .  I get an error message when I run latex on the file without "-shell-escape".
\newcommand{\Treebox}[1]{\Tr{\psframebox{#1}}}

\usepackage{amsmath,amssymb,amsthm,upgreek}

\newcommand{\stnd}[1]{\mathbb#1}
\newcommand{\R}{\stnd R}
\newcommand{\N}{\stnd N}
\newcommand{\Z}{\stnd Z}
%\newcommand{\lto}{\Rightarrow}
\newcommand{\lto}{\rightarrow}
\newcommand{\liff}{\Leftrightarrow}
\usepackage{mathrsfs}
\newcommand{\sig}{\mathscr S}
\newcommand{\str}[1]{\mathfrak#1}
\newcommand{\Forall}[1]{\forall#1\;}
\newcommand{\Exists}[1]{\exists#1\;}
\renewcommand{\leq}{\leqslant}
\newcommand{\included}{\subseteq}
\newcommand{\pincluded}{\subset}
\newcommand{\nincluded}{\nsubseteq}
\usepackage{bm}
%\newcommand{\class}[1]{\bm#1}
\newcommand{\gn}[1]{\ulcorner#1\urcorner}
\renewcommand{\phi}{\varphi}
\renewcommand{\theta}{\vartheta}

\newtheorem{theorem}{Theorem}
\newtheorem*{axiom}{Axiom}
\newtheorem*{lemma}{Lemma}
\newtheorem*{axsch}{Axiom Scheme}
\newtheorem*{corollary}{Corollary}

\renewcommand{\theequation}{\fnsymbol{equation}}

\begin{document}
\title{St John's College}
\author{David Pierce}
\date{\today}
\maketitle

This is a personal account of a place where I spent four years.

St John's College is an American private non-denominational liberal-arts college.  Its Great
Books program was instituted in 1937.  The College itself was
chartered in Annapolis, Maryland, in 1784, and one of its early alumni
was Francis Scott Key, who, after witnessing the failed British attack
on Baltimore in the War of 1812, wrote the poem that gave its words
to the American National Anthem.  Over a century later, in 1936, Key's
\emph{alma mater} was failing, and its governors brought 
in the reformers Stringfellow Barr and Scott Buchanan, who created the
Great Books program.  In 1964, the College established a
second campus in Santa Fe, New Mexico.  Students may transfer between
campuses, as indeed I myself did.

I matriculated at St John's College in Annapolis
in 1983, because of the line that today is found on the College's
website: 
\begin{quote}
  \textsc{The following teachers will return to St John's next year:}  Homer,
  Euclid, Chaucer, Einstein, Du Bois, Virgil, Augustine, Aristotle,
  Washington, Woolf, Plato, Tocqueville, Austen, Newton, Cervantes,
  Darwin, Mozart, Galileo, Tolstoy, Descartes, Freud, \dots
\end{quote}
Such authors\footnote{There is no fixed list of Great
  Books or Great Authors; the works read at St John's College may
  change somewhat from year to year.} 
   are read at the College in classes
of four kinds:
\begin{compactenum}[1)]
  \item
\emph{Tutorials,} in mathematics and in language, in each of the
four years of the undergraduate program; and in music, in the sophomore year;
\item
\emph{Laboratory,} in the freshman, junior, and senior years;
\item
\emph{Seminar,} every year, Monday and Thursday evenings, from eight till ten
o'clock or later;\footnote{It was so in my day; apparently now seminars in Santa Fe are half an hour earlier.}
\item
\emph{Preceptorials,} replacing the seminar for some weeks of the last two years.
\end{compactenum}
Teachers at the College are called tutors.  They do not
lecture.  Classes are discussions around a table, with excursions to
the blackboard or the laboratory bench by students as appropriate.  A seminar consists of
about twenty students and two tutors, who read and discuss books more or less chronologically.

The ideal of the seminar as I see it is to come to terms with the book
under discussion---be it Homer's \emph{Iliad,} Dante's \emph{Inferno,}
or Kant's \emph{Critique of Pure Reason}---without calling on
secondary sources.  All members of the seminar should participate in
the discussion, as in the deliberations of a jury.  One role of the
tutors then is like that of a jury foreman: to keep the discussion
from being sidetracked, and to ensure that quieter voices are still
heard.  Unlike a jury, a seminar need not reach a unanimous
conclusion.  A tutor starts each seminar with an Opening Question; but
this may be forgotten in the course of the discussion.

The \emph{ideal} is not to use secondary sources.  On the other hand,
until one reaches Chaucer in the sophomore year, all of the readings
themselves can be considered as secondary sources, because they are in
translation (from Greek, Latin, Hebrew, Italian, and so on).  One
function of the language tutorial is to address this problem.
Its
focus in the first two years is ancient Greek; in the last two,
French.  One learns enough to read in the original, or at least
translate, Plato and Homer, 
Flaubert and Baudelaire.  
One thus learns to be a bit suspicious of \emph{any} translation.
The tutorial is not the Greek tutorial
or the French tutorial; it is the language tutorial.  An important
aim is realized if the student comes to see what a
miracle it is that we can communicate at all.

I have not said it, but the reader may have inferred it:  there are no
electives at St John's.  All first-year students take the
freshman mathematics tutorial, so they all read Euclid and Ptolemy; in the
junior year they all read Newton.

The preceptorial \emph{resembles} an elective: each of the junior- and
senior-year seminar tutors leads a preceptorial, to which students are assigned
according to their preferences.  When I was a student in Santa Fe, the ideal articulated by the Dean of the College there was that the preceptorial
studied in depth a work that students had already encountered.  My preceptorials were on Plato's \emph{Republic} and Aristotle's \emph{Metaphysics}; a few others that I remember were on Kant or Flaubert or George Eliot.

The reader may wonder how students are evaluated.  From teaching at conventional universities, I have learned how concerned \emph{students} can be with how they are evaluated.  Perhaps the most important evaluation at St John's is \emph{self}-evaluation.  In any case, students \emph{are} assigned
letter grades, but these are not routinely told to them.  I myself did
not ask to see my grades until I had graduated from the College and
was applying to graduate school.  Grades at St John's are presumably based on written
essays, classroom participation, and individual meetings with tutors; there are no written examinations to base
grades on.

There \emph{are} a few examinations, oral and written, designed to ensure
that a student is technically ready to pass from, say, junior language
to senior language.  Twice a year, in the so-called Don Rag, each
student meets with his or her 
tutors, who discuss the student's performance in the third person.\footnote{According to a recent student handbook, the junior-year don rag is called a conference, and there is no longer a don rag at all in the senior year, on the grounds that seniors can judge their own performance.}
This causes some students not to
sleep the night before, or to flee from the event itself in tears. 

St John's College asserts that many of its graduates go on to achieve
success in fields such as law or medicine or even mathematics.  Early
in my time at the College, I met a student who was keen to become an
astronomer afterwards.  But I think she did not finish the College's
four-year program.  I myself cannot see any point in attending the
College for the sake of the degree at the end.  You attend because you
believe it is the place to be; you continue to attend because you are
moved by inner compulsion to do the work.   

Who wants to go to college to listen to what eighteen-year-olds have
to say about the most profound books ever written?  Not everybody
does.  I did. 

One might just as well ask, Who wants to engage a psychiatrist
just to listen to oneself speak?  Some people do, and
it can be worthwhile.  I say this in part from
considerations of the Freud that I read and discussed at St John's.
When I was a freshman I described the College as a kind of
psychoanalysis of civilization. 

There are truths that cannot be told to us by anybody else.  They may
be truths about our individual selves; they may be truths about
humanity.  If at the age of eighteen one is not ready to appreciate
all of the truths in Homer's \emph{Iliad} or Aristotle's
\emph{Ethics,} perhaps there is no purpose in having them pointed out
by a professor in a lecture.  At least if one has the experience of
reading the books oneself and talking about them, one is better able
to return to them later to find out more of what they have to offer. 

Johnnies---College alumni---\emph{do} return to the books.  They join
alumni seminars on the College's campuses, or in the various cities
where there are critical masses of Johnnies; they hold seminars by email or
so-called social media.\footnote{I have been part of a Johnnie email
  discussion list (currently constituted as a Google Group) for
  thirteen years.  I submitted a draft of this article to that list,
  and I am grateful to those members that read it.  Comments by Marion
  Billington, Bill Randolph, and Michael Schneider in particular led
  to changes in the article.} 

Again, why attend St John's in the first place?  Some of my own
motivation can be traced to my high-school sophomore year,
before I had heard of the College at all. 
My geometry class was rigorous: we proved everything, albeit in
the two-column, statement/reason format.  I developed the idea that
the real purpose of geometry was to learn, not about shapes, but about
logic.  Still I found something unsatisfying about our course and its
textbook.  I wondered why we did not just read Euclid.  I got hold of
the three volumes of Heath's translation, and I read some of Euclid's
propositions myself, though not in any systematic way. 

In the next two years I learned calculus.  When I found out about St
John's College, and I understood that freshmen there read Euclid, this
in itself may not have been an attractive point for me personally.
Euclid should be read, but perhaps in high school rather than in
college.  Still, better late than never.  In any case, after Euclid
there would be Ptolemy's spherical geometry, Apollonius's conic
sections, and so on. 

Meanwhile, I read Robert Pirsig's \emph{Zen and the Art of Motorcycle
  Maintenance.}  I came to share Pirsig's grandiose notion that the foundations
of Western civilization needed to be questioned.  St John's College
appeared to be just the place to do this questioning. 

Some colleges and universities try to attract students by
requiring them to take no particular courses.  Students
work out their own programs in consultation with advisors.  To me at
seventeen such a possibility was not an attraction.  I didn't know
much of anything; how could I pick and choose among various courses?
What would be the point of specializing so soon?  St John's College offered
the whole world.\footnote{One may quibble that this was only the Western world.  The College does have a graduate program in Eastern classics, instituted since my time.} 

Still, in the last two years of high school I was particularly fascinated
by mathematics.  We used Spivak's \emph{Calculus,} a book that does
not condescend, but treats its readers as fellow mathematicians.
Reading Spivak's chapter on the transcendence of $e$ was a mystical
experience. 

But at seventeen I could not see myself as being just a mathematician.
There was too much else to learn.  Also, while my calculus teacher
made me excited about mathematics, he was not personally admirable.  I
did not want to be like him.  I understood that mathematics was an
excellent escape from the uncertainties of adolescence.  But I did not
want just to pursue this escape. 

I performed well in a contest held by the mathematics department of a
local university.  The aim of the contest was to attract students to
that department.  At the reception after the awards ceremony, I did not then
feel as if my place was among the professors there.  One of them, not
knowing what else to say, asked me what kind of mathematics I was
interested in.  How could I know?  I was being asked to specialize,
not just in mathematics, but in some particular branch.  I was not
ready for that. 

An aunt recalled to me her college music
course.  She had known nothing about music before.  In the course, she learned
something completely new.  It filled her with elation.  In telling me
this, my aunt was probably trying to discourage me from just pursuing
something that I was already good at.  She may have been wrong to do
so, particularly if she herself had a prejudice against mathematics. 

And yet a marvelous thing about St John's College is the willingness of all students to take the complete program: to learn to read 
\begin{quote}
\selectlanguage{polutonikogreek}Kat'ebhn qj`es e>is Peirai~a met`a Gla'ukwnos to~u >Ar'iswnos,
 pros\-eux'o\-men'os te t~h| je~w| k`a`i <'ama t`hn <eort`hn boul'omenos je'asasjai t'ina tr'opon poi'hsousin, <'ate n~un pr~wton >'agontes
\end{quote}
and
\settowidth{\versewidth}{Comme les mendiants nourissent leur vermine;}
\begin{verse}[\versewidth]
La sottise, l'erreur, le p\'ech\'e, la l\'esine\\
Occupent nos esprits et travaillent nos corps;\\
Et nous alimentons nos aimable remords,\\
Comme les mendiants nourissent leur vermine;
\end{verse}
 to go to the blackboard and prove
\begin{quote}
If a cone is cut by a plane through its axis, and also cut by another
plane cutting the base of the cone in a straight line perpendicular to
the base of the axial triangle, and if, further, the diameter of the
section is parallel to one side of the axial triangle, and if any
straight line is drawn from the section of the cone to its diameter
such that this straight line is parallel to the common section of the
cutting plane and of the cone's base, then this straight line to the
diameter will equal in square the rectangle contained by (a) the
straight line from the section's vertex to where the straight line to
the diameter cuts it off and (b) another straight line which has the
same ratio to the straight line between the angle of the cone and the
vertex of the section as the square on the base of the axial triangle
has to the rectangle contained by the remaining two sides of the
triangle; 
\end{quote}
to read and discuss \emph{The Brothers Karamazov}; to perform the
Millikan Oil Drop Experiment and understand it as evidence for the
quantization of electrical charge. 

In high school I noticed that classmates struggling to solve an
exercise in Spivak were reluctant to ask me for help, though they knew
that I could probably give it.  They were competitive and wanted to
feel that they could succeed on their own merits.  Perhaps this was
not a bad impulse in itself.  But when I had been at St John's for a
while, I was impressed by the students who did ask me for mathematics
help, although they knew me
only by repute.  There was no exam coming up, there was no homework to
turn in.  The usual classroom procedure was for students to present
the reading at the blackboard; but students volunteered for this duty.
A friend once expressed satisfaction at having got through a
semester without having to go to the blackboard.  Other friends
pointed out that this was not something to be proud of. 

The number of freshmen on either St John's campus is a hundred or somewhat more.
My graduating class in Santa Fe was around fifty.  Evidently many
students may drop
out.\footnote{Apparently the drop-out rate in recent years has
  been much lower than before.}  When graduating, I did not know what
I would do next.  I 
decided to pursue a completely new kind of education: I went to work
on an organic farm.  I learned to spend all day out in the sun, bent
over, pulling weeds, looking under leaves for strawberries, digging
little holes for squash seeds; or riding on a hay wagon, getting
blisters and scratches as I stacked up the bales spat out by the
baler.  I became physically stronger than ever before, and I ate food
that my comrades and I had grown and harvested and cooked ourselves.  But I realized
that I had to study mathematics.  It would always fascinate me, and I
would suffer if I did not actually learn the subject as it was taught
today. 

Again, there are four years of mathematics at St John's, but learned
from original sources as far as possible.  This is not
always possible.  One needs a crash course in multivariable calculus
so that some sense can be made of Maxwell's equations of electricity
and magnetism.  One can however read Newton's own derivations of Kepler's laws
of planetary motion, because one has learned about conic sections from
Apollonius, as Newton himself did.  One reads Lobachevski as a
counterpoint to Euclid.  The latest work of mathematics that I read at
St John's was G\"odel's 1931 article 
`On formally undecidable propositions of {\emph{{P}rincipia
    mathematica}} and related systems'.\footnote{I read this in an
  extracurricular study group whose other members were tutors;
  this was in the summer before my senior year, when other students were not around.  In an
  earlier year I had joined a Kepler study group, initiated by a
  student and led by alumnus William Donahue, who was translating Kepler.} 

When I entered graduate school, I took graduate courses
right away.  I had taken an undergraduate analysis course in the
preceding summer, on the recommendation of my new department; but this
was frankly not challenging,\footnote{On my own I had already worked
  through some of Apostol's \emph{Mathematical Analysis.}} so after
that I went ahead with the regular graduate real analysis course.  I
never had computational or problem-solving courses like linear
algebra or differential equations, and probably I suffered for this, though it was not clear how.
I learned something of those subjects only when I was asked to teach them
later.  

As a teaching assistant given sections of a large calculus
lecture, I needed time to get used to leading a classroom and writing
quizzes.  I had little experience to draw on, unless I thought back to
high school.  I particularly did not like giving grades to students'
quiz answers.  I asked the students what \emph{they} thought of
the practice of grading.  One of them told me that grades helped him to
know how well he was doing in a course.  But
particularly in mathematics, students should be able to tell  on their
own whether they have solved problems correctly.  A solution is a
proof, even if it leads to a numerical answer.  The authority for the
correctness of a proof lies within each of us.  This is obscured by the
traditional classroom setup in which all students sit facing the
teacher. 

I had to sit that way myself in the courses that I took, and I found it strange.
Perhaps there was no alternative.  But I am sorry I did not get to
know the work of my classmates as well as that of my St John's
classmates.  I know what \emph I consider to be good mathematical
style; I know what publishers and journal editors consider to be at
least acceptable mathematical style.  But I do not know how well my
graduate-school classmates wrote, because I did not see their
writing.\footnote{A particular question I have is whether any of those classmates tried to fake their way through a proof.  Did they write something that a grader might accept, although they themselves do not understand it?  Sometimes I think the best thing I can do as a teacher is to induce my own students not to engage in this practice.}

At St John's I did not usually see the \emph{writing} of my classmates
either; but I heard them speak in class, and I saw them present
arguments at the blackboard.  I made such presentations myself.

For the last twelve years, I have lived at the eastern half of the
Mediterranean Sea, in what is now called Turkey, because the person I fell in love with and married happens to be from here.  Most of the books of the first two years of the St
John's program were written here, and this is one more reason why it is a
thrill to live here.  Having experienced an insistent Turkish
hospitality that may not take no for an answer, I feel as if I can finally
understand the first page of Plato's \emph{Republic,} where Polemarchus compels Socrates and Glaucon to stop by his house in the Piraeus.   

Part of the Turkish national mythology is that the Turks entered
Anatolia in 1071 after the Battle of Manzikert, and they took Istanbul
in 1453.  Even this late date is older than 1492, when Columbus sailed
the ocean blue and---according to the American mythology---discovered
the land where I grew up.  Still, a thousand years is not long in the history of Asia Minor.  It is a shame to limit one's feelings for this place to the last millenium.  Istanbul is mine now; it was mine in
1453; it was mine when Constantine founded it as Constantinople in
330; it was mine when it was Byzantium, and Xenophon passed
through with the remains of the Ten Thousand around 400 \textsc{bce}.  Centuries before that, somewhere down the coast, Homer composed the verses that I often read there today.
As John Donne wrote in the meditation that gave Hemingway the title of
\emph{For Whom the Bell Tolls,} `I am involved in \emph{Mankinde}'. 

Many people declare allegiance to a football team.  They care
whether their team wins or loses: it affects their happiness.  I do
not understand this passion very well.  On the other hand, I do have
my own team.  It includes anybody who has played the game of life and
left some record of what can be done with it.  At St John's College, I
spent four years pondering such records---poems, dialogues, treatises, plays,
novels, operas, paintings---in a community of people who were intent on
doing the same thing.  I could say the experience was a high point of
my life; but the experience is not over, nor will it ever be. 

Indeed, when I graduated from St John's, I told somebody that I had
learned to be happy.  That was a grand claim, and I am 
not sure why I made it.  It was premature, because of the
miseries that were to come as I tried to figure out what to do next.
But it seems to have turned out reasonably correct so far, as a
prediction of the role that the College would play in my life. 

Allan Bloom addressed our 1987 graduating class.  His popular treatise
\emph{The Closing of the American Mind} had come out recently.  From his address, I remember the assertion that we are
most human when we are reading great books with friends.  Now, this is just
what St John's wants to hear, and therefore a Johnnie should be leery
of it.  But I think there is something to it.  At any rate, St John's
either helped me to become myself, or made itself a part of me.

There may be many ways of feeling, if not fully \emph{human,} then
fully \emph{alive,} fully engaged, fully doing and being what one
wants to do and be.  A friend at the College described, in some such
terms, the experience of being drunk.  That is fine as far as it goes,
and indeed, if people are going to be
incorrigible alcoholics, it would be better to give them a place to
drink in safety, rather than in the gutter.  But perhaps
alcoholism should not be encouraged, while reading, thinking, and
discussing should.  Questions are raised about the value of education.
What is it good for?  It does not have to be good for anything.  Not
everything can be good for something else.  Some things are good,
simply.  The more people have those goods, the more the world is
better.  You can measure a society by average income, or car
ownership, or cell phone use, or years of education.  What
measure is best?  \emph{Is} there a best measure? 

I can propose freedom as the best measure, except that freedom itself
is not really measurable or even definable.
The last seminar reading for my class at St John's was \emph{The Adventures
  of Huckleberry Finn.}  Who is free in that book?
 Jim becomes free from legal slavery; but for him \emph{and} Huck and Tom,
becoming free from 
the \emph{habits} of slavery is not something that can be accomplished
by legal decree.  

I mentioned the freedom to choose electives
at conventional colleges and universities.  I am not sure it is a
freedom to be proud of.  But then I am convinced by the arguments of
Plato's Socrates: it is hard to know what we really want.  Students
are not customers who should be presumed to be always right.  If they
were always right, they would have no need for school in the first
place. 

At St John's there is no freedom to choose courses.  There is freedom
to question what one is told, whether by another student, a tutor, or a
book.  There is freedom to express one's own opinions, provided one is
then willing to face others' questions.  This is a freedom that can be
granted, perhaps, like freedom from chattel slavery; but the grantee
cannot be forced to take advantage of it.  This is why I do not
propose that all schools should be like St John's.  But schools like
St John's should be available. 

Sometimes at the beginning of a semester now, at my conventional university, I declare to my students that
mathematics is freedom.  Religions and governments try to impose
dogmas, making children recite formulas that they are supposed to
believe.  Mathematics cannot be so imposed.  It is not mathematics if
belief in it can in any way be imposed.  Mathematics must be freely
accepted through personal conviction.  But I cannot make
students believe \emph{this} just by telling them.   

Possibly I can \emph{show} them, or induce them to see it for themselves.
In recent years I have found the freedom to run a class like a St John's tutorial.  In
three semesters at two universities, I have had undergraduates go to
the board to present propositions from the likes of Euclid,
al-Khwarizmi, Cardano, and Newton.  But the student at the board will
often just address me, not the class; she or he may parrot the
mathematics without understanding it; classmates may not pay
attention.  Education for these students is still just something they
receive from a teacher, not something they demand from
everybody around them, \emph{including themselves.}  They have the freedom to
demand it, but they cannot be forced to do so.  Still, sometimes
students do raise questions, and discussions 
among them ensue.  \emph{Then} they are learning something. 

\end{document}
