a story by
Dr. Gates counted
heads with an elegant liver-spotted finger, carefully counted the
number of exams needed for each row, and handed them to the impatient
student in the front seat. Leo scanned the students sitting near him
for a girl with a large pocketbook tucked underneath her desk. When
he found one, sitting two desks behind him in the next row, he asked
her if she had a pen he could borrow.
Dr. Gates's thin
clear voice wafted to the middle of the room, where Leo was sitting.
"Please leave the examination papers face down on the desk until I
tell you to begin."
Leo thanked the
girl who had loaned him the pen and tested it on the back of his
bluebook. Then he tried one more time to make sure that his own pen
really had run out of ink. He was not superstitious or stupid enough
to believe that using the same pen for all of his exams would ensure
him good grades, but he was superstitious enough to believe that not
using the same pen on his last exam of the semester would jinx it.
All he had to do was complete his Philosophy 121 exam, and his junior
year of college would be over. He could go home. His car, a
miraculous survivor of his older brother's college days, was already
He leaned back in
his seat and stretched out his legs, ducking his sneakers to fit under
the book rack of the desk in front of him. He would drive with all
four windows down, the wind making a mess of the stuff he'd packed in
the back seat, riffling the pages of the textbooks he'd been unable to
sell back, flapping the sleeves of his shirts, bellying out the loose
bedding he'd thrown on top, and blowing loose car grit all over
everything. By the time he pulled into his parents' driveway, well
after dark, he would not be able to remember a single question from
any of his exams.
his lectern, Dr. Gates cleared his throat to get the class's
attention. Dr. Gates was tall, over six feet, thin, and old. His was
the only face Leo had ever seen in which the outline of every
supporting bone was visible. On the first day of class in January,
Leo had felt a small thrill in his stomach to see such an old frail
guy walk into the room to teach the class. He had known from the
first moment he saw him, dressed in a baggy suit of thick wool with a
plaid scarf still draped around his neck, that Dr. Gates would not be
full of shit. And Leo had been right. Three times a week, Dr. Gates
walked into Room 307 carrying a cracked leather portfolio and, after
greeting the class and making one remark about the weather, took a
single sheet of paper from the portfolio, laid the paper on the
lectern, and lectured for fifty minutes in his thin clear voice. He
lectured about Plato and Aristotle and Hobbes and Hume and Kant and
The Right and The Good, and he was not full of shit.
something different with your exam this time," he was saying. Leo
could see some of the people in the class looking even more impatient
than they had before, counting the minutes of their three-hour exam
period being wasted. "There is only one question on the exam for you
to answer," Dr. Gates continued, scanning the class, making random eye
contact. "I expect you to answer this question with a fully-developed
essay. And as I'm sure someone at some time must have told you, a
paragraph does not an essay make." He paused, and someone sitting
behind Leo muttered, "Oh, for Christ's sake."
"Please take your
time and think about the question carefully. This exam is worth half
your semester grade. It won't do for you to just throw down any old
thing." He paused again and then said, "You may turn over your exams
There was a
rustle of paper and then a loud intake of breath, as though the entire
class had gasped, in unison and on cue. In blurred elite type at the
top of the page was the heading:
Under this heading, typed neatly
without error or correction, was the question: How many angels can
dance on the head of a pin?
Leo picked the
paper up and flipped it over, then flipped it back. From the
crackling sound in the classroom, everyone else was doing the same
thing, again as if on cue. Leo laid his borrowed pen in the groove at
the top of his desk and waited to see what would happen next.
scraped against the floor, and he counted the number of people who
trooped to the front of the room, one, two, three, four, five, six,
each with the exam paper clutched indignantly in one hand, as if Dr.
Gates would not remember the single question he had asked. Leo waited
to see if his classmates would surround Dr. Gates's chair in an angry
mob, or if they would stand in a respectful line, still expecting to
receive an explanation of the question which would immediately give
them the answer. Or maybe some of them were expecting to be told that
the exam itself was all a mistake. Dr. Gates would reach into his
flaking portfolio and take out another one, a thick one with a
left-hand margin of neat lines on which you could write a, b, c, or
The students had
formed a line. I could live with that, Leo thought; I could do
multiple choice. The night before, after packing his car, he'd
studied for nearly two hours before falling asleep. He felt confident
of a C on a multiple choice, a possibly a B if there were a lot of
questions about Plato. Plato seemed to stick better than some of the
The first student
in line laid his exam paper in front of Dr. Gates and pointed to the
question. He leaned closer to Dr. Gates and whispered. I don't
know what you want. Dr. Gates whispered back, a little louder
than the student. I would like you to write an essay answering
this question. Think back on the material we have covered this
semester and the questions that were raised by it. That should help.
students were leaning forward, straining to hear what Dr. Gates was
saying. The student at Dr. Gates's chair did not move from the head
of the line. His finger did not leave its place on the paper. He
shook his head, and his voice was still low, but no longer a whisper.
But what do you want?
Dr. Gates shook
his head. I'm sorry. I cannot tell you any more than that. You
will need to think back over the questions we've raised this semester.
Oh, no, Leo
thought. Had there been a class in which Dr. Gates had given the
answer, and Leo, and a good many others apparently, had missed it?
Leo took pretty good notes, and he had not missed a single class, but
there must have been times when he wasn't completely attentive to the
lecture, when the room had been too warm, when he'd been tired and
fuzzy-headed from a cold, or when he'd simply had his own thoughts he
wanted to listen to.
He fiddled with
his pen. No one, not even a tenured professor, would base an entire
exam, half the grade for the course, on one or two sentences out of a
semester's worth of lectures. The idea was crazy, and Dr. Gates had
never seemed crazy before. In fact, one of the reasons Leo had not
missed any classes was that when Dr. Gates talked, what he said made
sense. It was logical.
The first student
in line picked up his exam paper and walked back to his seat. As the
second student in line stepped up to Dr. Gates's chair and laid her
exam paper in front of him and pointed to the question, Leo looked
around the room. There was only one person who was bent over his
bluebook writing. Everyone else was looking at the front of the
room. Although many of them were beginning to look decidedly pissed
off, they still had hope, if not faith, that they would end up not
having to take the exam Dr. Gates had handed out.
The girl was
shaking her head. Can you help me with this? Dr. Gates
nodded. Certainly. I would like you to write an essay answering
this question. Think back on the material we've covered this semester
and the questions that were raised by it. Does that help? The
girl shrugged and picked up her exam paper. I guess so. As
she went back to her seat, the other students in line turned around
and slunk back to their seats. Dr. Gates raised his head and said
softly, as though afraid of disturbing a room full of students working
on a difficult exam, "Are there any other questions about the exam?"
Leo felt the urge to laugh.
Suddenly a girl
sitting near the door jumped up and rushed out of the room. Catching
a glimpse of her white face, Leo hoped she made it in time. Karen was
a nice girl. He liked to talk to her before class, and a few times he
had helped her straighten out her notes.
More chair legs
scraped, and Leo turned around to see who it was. A short, muscular
guy, what was his name, George, Jim? He'd missed about half the
classes. He tossed his bluebook on Dr. Gates's desk on his way out of
the room. Dr. Gates pulled it toward him, turned it rightside up, and
opened it. Leo could see the straight lines of the F and the K,
slashes on the paper. Maybe Dr. Gates deserved it, but still, to
actually do it. Dr. Gates's face showed no emotion, and Leo looked
hard for it: a frown, a pursing of his lips, a clenching of his jaw, a
fleeting tic. But nothing. Dr. Gates reached into the inside pocket
of his jacket and took out a red felt-tip pen. He closed the cover of
the bluebook and made a mark on the line where the grade was to go.
Then he began writing something else. Leo at first thought it was a
nasty note of some sort, even though the student would never see it,
unless he came back and specifically asked to see his exam, and even
George or Jim would not be that stupid. Then Leo realized that the
guy must have been so pissed off that he'd neglected to fill out the
required information on the front of the bluebook and Dr. Gates was
doing it for him.
Now there's an
exercise in futility. The sentence popped into Leo's head but in
someone else's voice, not his own. It was a voice that seemed
familiar, but not one he recognized. Maybe someone off the TV or
someone from the dorm. Probably some windbag from the dorm said it
all the time, but it had never registered on Leo's brain until now.
Dr. Gates opened his portfolio again and took out a manila folder,
which he opened and laid on the front of the desk. He placed Jim or
George's exam neatly inside and replaced the grade book in his
The door of the
classroom opened, and Karen came back in. She was still pale, but the
color was starting to come back into her face. Leo tried to catch her
eye, but she was looking down. She walked straight to her desk,
picked up her pen, and began to write.
Leo looked at his
watch. Half an hour of the exam period had gone by. Time to get
started. He picked up his pen and wrote the required information on
the front of his bluebook. Leo Farnsworth, Philosophy 121, Section B,
Dr. Gates. Grade _____. He smoothed the paper with the flat of his
hand and read the question again. How many angels can dance on the
head of a pin?
What if, he
thought in what felt like a flash of inspiration, everyone answered
the question literally? How many angels can dance on the head of a
pin? Eight. Ten. Five hundred and thirty-seven. One billion and
fifty-two. If everyone answered with a number, any number, no one
could be wrong because if the medieval theologians who had posed the
question had found an answer, they wouldn't have spent years arguing
the question, now would they? His heart raced. If everyone answered
with a number, when no one number could be the right answer, what
could Gates do about it, flunk everybody in the class?
Of course Dr.
Gates could flunk everybody in the class. He could do anything he
wanted to. And if the Philosophy Department looked into it, someone
in the class would be honest and say that Dr. Gates's request for an
essay had been very clear. A fully-developed essay. If asked, Leo
would be that honest himself.
He laid his pen
back down. So much for inspiration. He didn't believe in it anyway.
He looked around at the other people in the room. A few more of them
had begun to write. The guy who had started writing as soon as Dr.
Gates told the class to begin was in two of Leo's other classes this
semester. Phil Marcone was a straight-A student, probably a genius,
because he didn't have to work at it. Leo had taken an instant liking
to him because whenever the class asshole decided to get pompous and
pontificate for five or ten minutes, Phil would put up his hand and
ask the professor a question, the answer to which would put him or her
right back on the track of the lecture.
Leo wondered what
Phil was writing. Whatever it was, Leo was sure it would be the right
answer. When he came back to school in the fall, he would have to
remember to ask Phil what he'd written on his philosophy exam. Phil
would remember his answer word for word. He might even offer to sit
down and type it out for Leo so he could take his time reading it.
Leo knew that by
the end of August he would never remember to ask Phil, but it was nice
to tell himself that he would. He continued to look around the room.
All but one or two people were writing. A girl named Linda, an art
major, was sitting next to him. She had been writing for quite a
while, and Leo now noticed that her hand wasn't moving in the right
direction; it was all over the paper. She couldn't be drawing
her exam? He craned his neck to see, hoping Dr. Gates wouldn't think
he was cheating. Linda looked up, glanced toward the front of the
room, and slowly slid her bluebook to the edge of her desk.
She had drawn the
pin with an oversized head, and on it Leo counted five angels, each
wearing a different type of robe. One of the angels wore priest's
vestments, another wore a toga, a third wore judge's robes. The
fourth wore a kimono, and the fifth angel, the smallest, wore a
knee-length bathrobe. All of the angels were dancing with streamers
flowing from their hands, and instead of halos, they had straight rays
of light pouring from the tops of their heads. Linda pulled the
bluebook back and wrote something at the bottom of the page. Leo knew
what she was writing: Here they are! How you interpret them is up to
you. It was the same thing she said whenever anyone asked for
an explanation of a drawing in the sketchbook she always carried with
her. As she stood up to leave, she looked at Leo, grinned, and drew
her finger across her throat.
As soon as Linda
had shut the door behind her, another chair scraped. A girl wearing
tight jeans and flats which clicked loudly against the tile floor
walked to the front of the room. Leo watched her lay her bluebook in
the folder and lean over to Dr. Gates and whisper. Have a good
summer, Dr. Gates. Her little red pocketbook bumped against her
hip as she walked from the room.
himself from looking at his watch. Panic was not going to help. He
needed to be logical. He had to write down something that made
sense. This was his last exam of the year, the only thing he needed
to finish before he could drive home.
If he were going
to be logical, the first question he needed to answer was, Do angels
in fact exist? He scrawled the word "existence" on the inside cover
of his bluebook and underlined it. The beginning of an outline. He
wrote "I." to the left of "existence."
He seemed to
remember from lecture that someone had once used a syllogism to prove
that angels exist. He could use that. But he couldn't remember the
guy's name or anything he'd written or even the century he'd lived
in. Leo closed his eyes and tried to visualize the pages of his
notebook. All he saw was page after page of yellow highlighter. The
lines of highlighter were clear in his mind, shaded and wavy, like
watercolor; however, there was nothing written underneath. He glanced
at the entry of his outline, "existence," to see if that would help
jog his memory.
remembered was that the guy whose name he'd forgotten had not proven
the existence of angels but the existence of God. But if he could
prove the existence of God, couldn't he prove the existence of angels
because they're all in Heaven? That doesn't prove jack, he told
himself, because then I'd still have to prove that Heaven exists. And
it's a moot point anyway because I don't remember the name of the guy
who proved God exists.
movement out of the corner of his eye. A group of people, five or
six, possibly more, walked to the front of the room and laid their
completed exams in the folder. When Leo saw that the girl who had
loaned him the pen was among them, he held it up. She mouthed, Keep
it, and left with the others.
He looked back
down at his bluebook. He had written only one word in it,
"existence," and that was on the inside cover, not where it counted.
The only way he could prove an angel existed was to see it, and
then he'd have to photograph it because no one would believe him
otherwise. Even then still no one would believe him because they
would assume he'd faked the picture.
in futility. He wrote "faith" under "existence" on the inside cover
of his bluebook. Take it as a given, he told himself. I'll take it
as given that they exist. But then what are they? What form do they
take? Are they creatures with a physical body, or spirits? He
doubted they were physical beings; otherwise there would be a lot more
reports of angel sightings. And if they were spirits, they couldn't
be the same type as ghosts. He'd heard of angels guarding people but
never haunting them. But I don't believe in ghosts, he told himself.
His head was beginning to ache, and he wondered if he would still be
able to pass the course with an F on the final. On the midterm he'd
made an 87; an F on the final would give him 69 points. Averaged
together, that would be a 79 for his final grade. Passing. But to
get the 69 points, he still had to write something. Handing in an
empty bluebook would give him nothing.
All right, then,
taking it as given that angels exist, their form is not human, nor is
it creature or ghost or spirit, but something else. He had no idea
what, except that whoever had first posed the question thought they
were small enough to dance on the head of a pin.
Now, his mind
continued, are angels able to dance, and if so, why would they want
to? If I can assume that they exist, which no one has been able to
prove, in a form that is unknown, I can assume they can dance. Why
the hell not? The second part of the question was more difficult to
answer. Why would they want to, or more specifically why would they
do it on the head of a pin? Couldn't they find some place better?
Moreover, the struggle to keep from knocking the other angels off the
pin or poking them in the ribs, which of course he was unable to prove
they had, seemed a lot more trouble than it could possibly be worth.
He wrote "III."
under the "II." and next to it "desire." Then he crossed out "desire"
and wrote "volition." Assuming that angels exist, in a form that is
capable of dancing, and further assuming that they have the desire,
the volition to dance on the head of a pin, the number of
angels who could it would depend on the type of dance they were
doing. As he studied what he had just written, Leo saw reproduced in
his mind the pages of a book. However, they were not the pages of his
notebook as he had hoped. The type was set in a column running down
the center of each page. The rest of the two pages was taken up by a
color illustration of the cross-section of a house. In one room of
the house a man with yellow hair and very long arms was pounding nails
with a hammer. Running wildly through the other rooms were a cat and
a rat and a dog. This is the dog that worried the cat that killed the
rat that ate the malt that lay in the house that Jack built. Leo
leaned back and closed his eyes, rubbing them gently with two
fingertips until the pages of the book dissolved.
He passed his
hand through his hair and looked up. No one was sitting in front of
him or beside him. He turned around. There was no one sitting behind
him either. The stack of completed exams in the folder on Dr. Gates's
desk was nearly four inches high. Leo looked at his watch. Two and a
half hours of the exam period had gone by. He had half an hour left.
He looked at Dr. Gates, who had his head down, reading a discolored
paperback. Dr. Gates looked up from the book, keeping it spread open
with his thumb and ring finger. "How are you coming, Leo?"
written a single word. I'm sorry to be holding you up."
"Take your time.
The exam period doesn't end until twelve o'clock." He smiled
encouragement and bent his head to read again.
Leo looked down
at the blank first page of his bluebook, then at the three words which
comprised his outline--existence, faith, volition--then at his watch,
then back at Dr. Gates. He cleared his throat. "Dr. Gates?"
Dr. Gates looked
up. "Yes, Leo?"
"What are you
actually. My first grandchild is due next month, and it's been over
thirty years since my wife and I have had a baby in the house." He
abruptly stopped speaking and looked down at the book.
Leo again felt
the urge to laugh. He'd seen this Dr. Spock on TV a few months ago,
when he was in the dorm lounge wasting time, watching Hour Magazine or
Donahue or one of those shows. Dr. Spock was old, too, Dr. Gates's
age, possibly a few years older. He was a child expert, and everyone
in the 'fifties had a copy of his book and raised their kids according
to his theories. Then after the kids had grown up, Dr. Spock got on
TV and said his theories were all wrong!
Leo began to
The answer to the
question How many angels can dance on the head of a pin is of course
that there is no answer. Back in medieval times, the theologians
spent many years arguing about this question and couldn't find the
answer. They spent a lot of time and energy on this question. Some of
them might have even devoted their whole life to finding the answer.
Yet nowadays in modern times the only time one hears this question is
when a person uses it to show that arguing about a certain question is
pointless and stupid. For example, you might say that arguing over how
many nuclear weapons a country should have is like arguing over how
many angels can dance on the head of a pin. When three of these bombs
can wipe out the entire world, what's the point in arguing over
whether a country should have a hundred or a thousand or a million of
them? It's stupid and it doesn't get you anywhere, like arguing over
how many angels can dance on the head of a pin.
The point of
studying Philosophy or I guess any course is to find out what
questions are important and what questions aren't. For example, in
this Philosophy class, one of the things we studied was what each
philosopher thought was the Right and the Good. What is the Right and
the Good is an important question to ask and to find the answer to
because that's how you're going to live your life.
He dropped his pen on the desk, flexed
his hand, and looked at his watch. One minute left. He began a new
For myself, I think
this was a good exam question because it made me think about whether
angels really exist. I'd seen them on TV and in Bible study books, with
wings and halos, but they weren't real. Thinking about angels for this
exam made them seem real to me, and I think I would be glad if I found
out some day that they really do exist.
Leo stood up, and
as he walked to the front of the room, tried to think of what he could
say to Dr. Gates, sitting there reading an old edition of Dr. Spock,
which was now wrong. He laid his exam on top of the stack. "Here it
is. Finally. I'm glad that's over with." He neatened the stack, which
had started to slide. Dr. Gates smiled. "I'll be interested to read
these. I hesitated to give an exam like this, but you get tired of
reading your own words coming back at you year after year. Only
garbled. You start wondering if maybe you really do sound like that."
He picked up the folder, wedged it into his portfolio, and stood up.
"Good luck with
your grandchild, sir," Leo said.
Dr. Gates slipped
the paperback into his jacket pocket. "Thank you."
They walked out of
the room together, and Dr. Gates waved as he pressed the button for the
elevator and Leo continued down the corridor to the stairs.
As he pulled into
mid-day traffic and the warm spring breeze blew through his car, Leo
hoped that after Dr. Gates had gotten home and eaten his lunch and
chatted with his wife, he would read Leo's exam first.