Thoughts for Discussion
on
Mathematics and Computing
Tim McLarnan
During the past few months, I’ve been trying to think about where
my future lies at Earlham. Am I a mathematician, or a computer scientist,
or an amphibian? Mic has been trying both to press me to attain clarity on
this point, and to back off to let me reflect. I very much appreciate both
parts of this effort.
By now, though, it is clear that I need to come to a decision if we are
to make a intelligent hire this year; and I have made a decision. At
bottom, I am a mathematician. For the time being, I’m prepared to
continue teaching some classes in CS, but I’d prefer not indefinitely
to be half time in Math and half time in CS. At some point in the future,
I’d like to be free to step away from CS altogether, and I think this
path or something close to it may be both desirable to me and in the best
interests of our students. If one impact of this decision is that I’m
not the best person to hold the Tremewan chair, then I have no objections
whatever to using one of my own chairs instead.
Having written all that, I’m also a realist. I get paid to teach
what the students need, not what most interests me at any given moment,
and that’s probably a good thing for everybody. It will probably
be the case that I’ll continue to be needed in CS over the near
and maybe medium term. I’ll therefore teach CS over that period,
and I’ll probably even enjoy it. I’m certainly psyched to do
CS this year. I think it would be in everyone’s best interest,
though, if we could contrive a plan under which I am not committing now
to be doing CS half time in the year 2020.
That’s the executive summary of this document. Skip the rest of it
if you’re busy. Most of the remainder is a meditation as much for
myself as for others on how I view CS today. I hope at some point to chat
with some of you on this essay; but don’t feel compelled to look at
it now. You might just glance at what I say at the very end about
staffing, though.
It has taken me a long time to come to this decision. I have a real love
for computing as a mathematical discipline, as an application of the
science of algorithms, and as a form of engineering in which amazing
creations are formed from “pure brain stuff,” as I think Fred
Brooks says. I enjoy Earlham’s CS students, in part because their
intellectual approaches and concerns are in many cases so different from
mine. I consider Charlie Peck a close friend and an esteemed intellectual
companion. I have learned much in my past few years of involvement in CS
that I consider exciting and beautiful. I also like to hack. There is,
however, another side to my attitudes toward computers and computer
science. It has taken me some time to see how deeply ambivalent are my
feelings about computing and its future. The remainder of this document is
an attempt to clarify for myself and for my friends the degree and origin
of that ambivalence.
For me, mathematics possesses in and of itself transcendent value. In
mathematics, we can actually know, and what we discover is actually
universal. It is our glimpse of the infinite. It is the sign that we are
made in the image of the divine logos. In my prayers, I give thanks to God
above all for the beauty and wonder and subtlety of the eternal world we
uncover bright flashes from in mathematics. (I realize, of course, that
I’m making lots of bald assertions here in religious language we
don’t all share. My point is not that we all need to agree on these
controversial assertions, but it is important in describing my intellectual
life to understand that I do make these claims.)
I like CS, but I don’t feel the same way about it. For me, computing
is precisely described as Pascal described geometry: it is, says Pascal,
the most beautiful trade in the world, but it is only a trade. At bottom,
computing possesses value as a tool to serve some other end.
In its early days, the end served by computing was mathematics, and it
was this service that drew me naturally into computing. I remember the day
in 1975 when I was shown an early version of what became the computer
algebra system Axiom. One of its designers, David Y. Y. Yun, asked
the system to compute a 
Vandermonde determinant:
The result is a polynomial with 24 terms, none of the same degree in
all 4 variables. David then asked the computer to factor this polynomial,
turning to me at the same time and asking what the factorization was. I
said I had no idea, but David pushed me, “You know enough linear
algebra. How does it factor?” As I tried to think, the computer
printed the reply:
The moment I saw that answer, I knew what the general theorem was, and
how to prove it. (After all, the determinant vanishes if any 2 rows are
equal.) I also knew that the future practice of mathematics had been
utterly changed. We now possessed a tool of enormous power for
mathematical exploration and discovery.
If computers arose as tools for mathematical investigation, though, it is
hard now to argue that they now principally serve science. Although there
remain pockets of light, the vast expanse of the computing industry today
seems to serve altogether other interests. We manage corporate wealth and
enable organization on larger and less human scales than ever before. We
help millions of people to escape the reality of God’s creation in
video entertainments. We empower vast new efforts at marketing and
advertising. We move trillions of packets daily, billions of them actually
not pornographic. Society views these efforts with wild intoxication. The
computer is the greatest creation of our age.
I have no nuanced and coherent social philosophy with which to judge all
these developments, but my naive reaction as a simple human being is that
much of this is unnecessary, much is not ennobling, some is not moral, and
none of it is interesting. Drawn to a discipline that promised liberating
power to the human mind, I have seen it transformed in the service of
blind acquisition. Intending to free humans to discover deep truths, we
have ended offering shallow and tawdry temptations that advance only greed
and that end in spiritual bondage. I have no interest in spending my life
to further this effort. A tool to give people eyes to see mathematically
attracts me mightily; a tool to provide video entertainment and enrich
Walt Disney repels.
I’m aware as I write this that I am being too hard on the computer
as electronic medium. There is still on the Internet much that is good and
useful and liberating. But it helps me to articulate explicitly just how
conflicted I find myself in the presence of this side of computing.
That I should hold such a skeptical attitude about computers probably
shouldn’t be surprising. My sentiments about technology in general
are equally divided. I don’t own a television or a VCR or a cell
phone or an answering machine. My old rotary dial phone has never broken,
and I haven’t seen any need to replace it. I don’t like cars. I
don’t do voice mail. I’ve thought seriously about moving the
refrigerator into the garage in order to get the noise of the compressor
out of the house. I once had a camera, but I stopped using it as an
expensive and inelegant machine coming between me and the world.
Computers seemed to me to be different, and to some degree I still think
they are. A computer represents appropriate technology for mathematics, a
telescope for the mind, a device crafted with elegance on provable
principles and serving the end of understanding. It offers fantastic power
to explore.
To a great degree, though, the current evolution of the computer moves it
farther each year from this vision of an elegant and reliable tool for
investigation. Each year, operating systems grow more massive, with more
layers of emulation supporting larger numbers of archaic protocols.
New gee-whiz features are pasted on, complicating programming and bloating
systems without adding anything useful. Stability, elegance, openness, and
comprehensibility are all secondary goals (if that) before the drive to
add bells and whistles. Each release of MacOS adds bulk and bugs. Windows
98 is Windows 95 minus the stability. Linux promises an alternative, but
it is larger than any of these alternatives, and to make a fresh
installation out of the box work seems to require days of tinkering.
Oberon offered an alternative, but before achieving stability it, too, was
swept away by the rush for new features. Java makes promises, but it does not
yet seem to run efficiently and reliably on any platform, its own
libraries have Byzantine complexity, and in any case, it sits atop our
profoundly diseased operating systems.
For me, computers and software have the same allure of school supplies at
the beginning of the year. Armed with these beautiful pencils, this
colorful ruler, this soft eraser, and this clean paper, I used to think,
I’ll be happy and efficient and brilliant this year at last. I have
the same delusions about computers. With each installation of a new OS and
compiler, I imagine I’ll finally have a stable environment in which
development is efficient and reliable and pleasant. But this has never
happened, and in my more lucid moments, I no longer expect it to happen. I see no
one prepared to declare a moratorium on features and backward
compatibility in order to create a truly simple and truly reliable
environment for the future. There is no market for such a thing. Yet this
is what I keep looking for and keep deluding myself that I have found. If
I just learn one more language, install one more system, buy one more box,
I will at last be happy.
This is really an awful temptation for me. Mucking about with
computers—and learning useful and fun things about them which have
impact on my teaching of CS—takes an enormous amount of my time and
money and energy. Is it not more prudent to spend this time rather on
mathematics, the science I’m allegedly amassing these school supplies
in order to practice? Or on my family? Or on the world? Is it not shocking
that I own a variety of tools for writing mathematics by computer and that
I used them incessantly before discovering in a quick test that none of
these tools was even half as fast for me as writing with a pen on
paper?
For me, in short, computers are superbly useful tools, but they are also
an enormous, almost crippling distraction. As I grow older and life grows shorter, the amount
of time I am (or should be) prepared to devote to the latest cool new tool
that will finally give computing the stability and power it has always
lacked grows less and less. This is doubly true as these tools themselves
grow more and more complex and as they are more and more tailored to serve
goals with which I am profoundly unsympathetic. I do not think that over the
next 2 decades I can maintain the level of interest an energy and
enthusiasm—should I say delusion?—needed to stay effective and
current in a business whose appeal for me is diminishing. We will do
better if we can find someone whose passion for CS is stronger than mine,
whose life is centered here as mine is not.
Having said all this, it is still not that easy for me to let go of the
discipline of CS. There is too much good there, and I’ve had too much
fun with it. It’s relaxing compared to mathematics. I hate to give up
and abandon a lovely child of the human intellect to serve ignoble ends.
But I haven’t the energy and focus and position from which to remake
the computing industry to meet real needs with well-designed tools, nor
are our students best served if their education is primarily in the hands
of a dinosaur, an Amishman, a voice crying in the wilderness.
All my life, I’ve been an intellectual wanderer—a
mathematician, a mineralogist, a chemist, a computer scientist. Some of
that wandering has happened for good reasons. I find many things beautiful
and exciting, and I learn new things quickly. Some of my nomadism comes
from darker sources, though. I’m afraid to take risks, and rather
than venture all in mathematics, which is so important to me, I shrink
away and play at games with lower stakes. In the end, though, mathematics
is and has always been the center of my academic existence, whether at any
moment I realized that fact or not. I was right to return to mathematics
from geochemistry, and I am right today to recognize mathematics as my
mind’s true home. The pull of peripatetic adventurism is always with
me, but so is the voice of my first love, declaring that purity of heart
is to will one thing.
Where does this leave us on the second floor of Dennis Hall? The short
answer is that I’m not quite sure. I’m just figuring out my own
desires, and have not yet spent much time thinking through the details of
how to make them possible, or of whether they are possible. Here are a few
data points.
- I’d welcome the chance to talk with some or all of you about the
contents of this document which is very much a paper for discussion and
not a finished plan for my life.
- In saying that I’d like to shift my focus toward mathematics,
I’m not ignoring the fact that I have current commitments in CS. I
will clearly be primarily a computer scientist for this year, and in some
sense that’s as far ahead as we know the staffing picture. There are
courses like Theory or Algorithms that I might well be happy to teach in
perpetuity. My philosophic desires have to take second place to the
teaching needs of the College, which pays me to educate students, not to
achieve nirvana. There are plenty of things I’d rather not do that
are nevertheless part of my job.
- It would be simpler for our hiring this year if I were eager to be a
permanent 50% computer scientist. Can we attract a strong mathematician
(which I think we want) who is also excited about permanent significant
involvement in CS? Should we contemplate a CS hire who can do some courses
in mathematics on the side? Do we go for a straight-up mathematician and
plan for a future in which Charlie will eventually take over some of my CS
course load? I have more questions here than answers, but we all need to
think carefully (and somewhat quickly) about these.
Many thanks to anyone who may have waded through my half-formed thoughts;
I hope we’ll have a chance to think further about them together.