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Title: Math/Number Theory/Prime Numbers - Bipeds and Prime Numbers Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity. (September 18, 2001)
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ref.: grad.doc
Address by Professor Garrett Barden Former
Professor of Philosophy, UCC At the Conferring of
Degrees in the Faculties of Commerce and Science at
10.00 am and 12.30 pm on Tuesday, 18 September, 2001
Bipeds and Prime Numbers
In his novel, Pictures from an Institution,
Randall Jarrell describes the graduation address at a girls'
college in New England.
Here is part of the account:
Mr Daudier spoke for -- for years, we felt... Gertrude had
heard him give the speech before; so had I; Gottfried never
had; yet Gottfried knew it better that we did, because
Gottfried was older than we were, and had heard that speech
more times than we had.1
Despite this nearly unavoidable element we still have the
graduation address; we seem to be the kind of beings that need
to mark those periodic occasions when a shift is made in a life
between one stage and the next. The graduation ceremony is a
rite of passage.
My title comes from the plaque attached to the body of NASA
deep space probes. To tell other beings of us the text, in the
translation that I know -- the original is in symbols -- says
that we are
`bilaterally symmetrical, ually differentiated bipeds
located on one of the outer spirals of the Milky Way, capable
of recognising the prime numbers and moved by one
extraordinary quality that lasts longer than all our other
urges -- curiosity.'
What other beings will make of the symbols we can hardly know.
What can we make of it? Like any description of reality it makes
choices; it puts things in and leaves things out.
Graduation is the ritual celebration of a successful step. From
undergraduate to Bachelor; from Bachelor to Master; from Master
to Doctor. Every study is an ordered set of questions and so
every study is driven by curiosity. For the past few years
ordered curiosity has been one of the driving and organising
forces in your lives. Not, of course, the only one but still
one. Graduation, then, is a celebration of curiosity.
In the text curiosity is said to be a `quality that lasts
longer than all our other urges'. Were curiosity not an urge,
universities would not exist but the natural urge is not enough;
there is a fundamental choice involved here and it is this
choice, not simply the natural urge itself, that is at the root
of our civilisation. Our civilisation is the fruit of many
choices -- some good, some bad, some intelligent, some immensely
stupid, some kind and some consumed with hatred; one of them is
the decision to give free rein to curiosity; we have decided
that enquiry is valuable for its own sake. That decision is not
irreversible. Indeed, in different ways it is often attacked.
But at graduation we celebrate it.
We are bilaterally symmetrical and ually differentiated
bipeds. As are apes. We are curious but so are apes. To describe
us as bipeds is one of the choices made in the text. To describe
us as curious is yet another. What of the statement that we are
all `capable of recognising the prime numbers'? Not all of us do
recognise them. Not all human cultures and civilisations do
recognise or have recognised them. The choice of this feature in
the description is startling. It is, obviously, a choice made by
people within a civilisation where prime numbers are recognised.
But the writers need not have chosen them.
`Bilateral symmetry', `ually differentiated bipeds',
`curious' -- these are fairly predictable. `Capable of
recognising the prime numbers' wakes us up. Imagine a group of
intelligent aliens coming across a probe. They would be curious
about it because curiosity is simply the manifestation of
intelligence. Suppose that they had succeeded in deciphering the
symbols. Being intelligent they would be capable of recognising
the prime numbers because that is a capacity of intelligence but
suppose that they had not yet recognised them. What would they
make of this unknown object `the prime numbers'? They would
assume that these unknown objects were of immense importance to
the civilisation whence the probe had come. Had they discovered
numbers and mathematics they would infer that mathematics was
central to that culture. And, of course, the probe itself is a
message.
We do recognize the prime numbers are and we appreciate
something of their importance and fascination. We recognise them
because our forebears did and passed mathematics on to us. In
short, we recognise them because we have been educated; that is,
brought into the civilisation. At graduation we celebrate not
only curiosity but also the tradition into which we have been
educated.
Our intellectual tradition is profoundly mathematical and, ever
since the Greeks and even the Babylonians, mathematics has been
the central symbol of enquiry -- the word in Greek originally
meant `learning'. So the choice of prime numbers is both good
and traditional. A culture is a way of being in the world and
ours is an immensely differentiated culture beyond the capacity
of any single mind; we are co-operatively responsible for it.
Intellectual responsibility is care for the world through taking
care of thought and language and the graduate is responsible
particularly for that part of the civilisation in which he or
she has become learnèd.
At a graduation we celebrate the intellectual life and the
achievements of the new graduates.
Less obviously, we celebrate the assuming of responsibility.
`To graduate' doesn't mean `to have passed an examination' -- it
does of course include that -- it means to have passed from the
state of pupillage to intellectual hood with its attendant
responsibilities.
For different things we are differently responsible. For a
precious object handed down to us, say, a great painting or
sculpture, we are responsible for its safekeeping and for
passing it on intact to the next generation. The civilisation as
a whole is not an object of that kind; the tradition -- that
which is handed down -- is not something finished that is to be
handed on intact. This is the route of stagnation and the way of
the reactionary who `pulls [the past] out of the sphere of
vitality, and, thoroughly dead as it is, he places it on the
throne so that it may rule over our souls'2 Because the civilisation --
what is handed down -- is the fruit of curiosity, to be
responsible for it is to carry it forward curiously.
Sometimes we use the word `tradition' as if what it referred to
was to be kept inviolate and unchanged; as if the tradition were
a thing to be treasured like a sculpture or painting. But, in
the intellectual life [not, of course, only in the intellectual
life but utterly central to the intellectual life] , learning
the tradition is learning what has been discovered so far,
sometimes rediscovering what passing fashion has forgotten.
Learning the tradition is learning how to examine received
knowledge critically -- for great discoveries often begin with
the suspicion that what has been taken for granted need not be
taken for granted but may be mistaken. Learning the tradition is
learning how to carry the tradition forward. When we try to
carry the tradition forward we turn from what has been
understood and, carrying the tradition within us, turn to what
is yet to be understood; from questions that have been answered
to questions that have not been answered and to questions that
have not yet been asked. But to ask a question is to assume
responsibility for it and, through it, for the world about which
the question is asked.
Newman, in his The Idea of a University, wrote
that university graduates would not by that fact be better, more
moral, people. And yet, when the Dean calls a class forward for
conferring, he vouches for the students as `fit for graduation
both in morals and in learning' [idoneous...tam moralibus
quam doctrina]. And I have been talking of responsibility
which is a moral demand. Newman was, I think, speaking of the
moral life as a whole and there he was quite right; learning
does not confer goodness. But it does make a very specific
demand just as does each profession.
You are graduating in the intellectual life and your general
responsibility is for its development. Others may graduate into
that life less publicly, less formally, less institutionally,
for the intellectual life, is not confined to university
graduates. But that life is formally and publicly yours and
others may rightly expect of you what they need not always
expect of others. Your very specific responsibility is to retain
and develop your curiosity; to remain always a student even if
no longer a pupil. Without critical curiosity, as the servant in
the Aeschylus' Choephori says, `the dead kill the
living'.
I have been commenting on the NASA description of ourselves.
Like any description, it is the result of choice and that
inevitably requires both inclusion and exclusion -- choice, as
economists say, involves cost, that is, whatever is foregone.
What does the description exclude? The obvious, but somewhat
unenlightening, answer is that it excludes everything that it
doesn't include.3 It mentions
the capacity to recognise prime numbers but make no reference to
the capacity to make ice cream. There is, however, one hugely
important aspect of ourselves excluded or only obliquely
included: our capacity for feeling. If it is present at all, as
some may think it is, in the reference to ually
differentiated bipeds, it is present only as a shadow. You may
remember the Vulcan, Mr Spock,4
in the early Startrek. Vulcans were presented as
wholly intellectual; the NASA description fits them perfectly.
What Spock lacked was feeling or emotional response. This lack
was a significant element in the story; it is also a significant
exclusion from the NASA description of ourselves. But it is not
immediately startling. Certainly it did not strike me until I
began to think about exclusions. Exclusion of intellect in even
a brief description of humans would strike us as odd. So why are
we not immediately struck by the exclusion of feeling? Properly
to answer that question would be difficult anywhere and
impossible here. I would suggest a general and sketchy answer:
our civilisation -- that is, the civilisation of the West -- has
not well integrated feeling into the account of the human and we
are the heirs of our tradition. There are, as Pascal's aphorism
says, `Two excesses. Exclude reason, admit only reason.' 5 Intellectual responsibility
requires the avoidance of both.
Universities are immensely expensive institutions often paid
for by those not in them including many who have not directly
profited from them. That is one reason why your knowledge is not
unambiguously yours. But there is a deeper reason that I can
best express in metaphor. When you undertake the intellectual
life you don't own it; it owns you. To become intellectually
responsible is to allow enquiry to take you over. And this is
the final thing that we celebrate here to-day.
There is a small feast after this and many of you will go on to
other feasts. We celebrate two kinds of things with feasts.
There is the feast to mark something done and finished -- a
match or competition won, for example. But we also feast to mark
something taken on -- marriage, for example. To-day's feasts
celebrate both: an achievement, work properly done, something
worthwhile accomplished; a responsibility taken on. And so there
were two parts to what at the outset -- years ago you feel -- I
said that graduation speeches were about. The first part is
congratulation; the second is or, in the tradition used to be,
and may still survive in a hidden way that we hardly notice when
we say `Best Wishes' - blessing. Blessings were commonplace in
the Torah or Old Testament. I don't know when they
went out of secular fashion but, because I have spoken of
tradition, I shall risk taking them out of hiding and say ,
first, Congratulations on work well done and, finally, Go, with
our blessings on your heads.
Jarrell, Randal: Pictures from an
Institution, [1952]; reprinted by Meridian, New
York, 1960, p.237
Ortega y Gasset, José:
Meditations on Quixote, [1914] Norton, 1963,
p.49
There are, of course and necessarily, other
things excluded. No mention is made of humans being social
or political animals -- a definition famous from Aristotle.
We feel because we are animals and feel as we do because we
are, in the old term, social and rational animals.
More accurately, I am told, `the
half-Vulcan, Mr Spock...'
4 Pascal, Pensées,
[between 1555 and 1562] Lafuma, 368 Deux excès.
Exclure la raison, n'admettre que la raison. Quoted
in François Monconduit: `Comment penser le vertu du
citoyen en démocratie?' , mss. Paris, n.d.
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Graduation | address | by | former | professor | of | philosophy | Garrett | Barden. | Mentions | primes | as | sign | of | human | curiosity. | (September | 18, | 2001) |
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http://www.ucc.ie/opa/conferspech/gbarden.html
Bipeds and Prime Numbers 2008 November
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Graduation address by former professor of philosophy Garrett Barden. Mentions primes as sign of human curiosity. (September 18, 2001)
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