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September 8, 2003
Ted Wong (Biology)
"Why Quantify; or, Why the World Is Not Enough"
Summary
Prepared by Anne Dalke
Additions, revisions, extensions are encouraged in the Forum
Participants
Ted began our conversation with several claims and illustrative graphs:
that when scientists see patterns in the world, the order they
describe takes the form of mathematical models, which have to be
numerical in order to be testable. Scientists go to nature and
extract numbers; measurement mediates--that is, inserts a process
and so stands between--nature and science. These techniques of
measurement are not completely transparent, but have a structure and
life of their own, which affect how we think. The translation of the
world into numbers changes what we are describing.
Ted's particular area of research is plant architecture; he asks
repeatedly why they have the shape they do, why they grow to fill
spaces, how they come to have the plasticity to grow in different
directions. Architecture, which is so important in plant ecology, is
very difficult to talk about it and put on paper. For instance, a
favorite activity of scientists is to draw graphs, with one axis controlled
and one variable. But it is difficult to fit the narrative
of how a tree grows into a graph. The story is too high-dimensional;
there is too much information, even in the ratio of probabilities for
branching, to reduce to numbers. Plant architecture cannot be
studied in its full complexity only using statistics.
Ted then invited us to reflect more generally on how our thinking is
shaped by particular mathematical tools. Suggesting that our
"knowledge is an artifact of method," he described the development of
a new method (called "a pressure bomb") for measuring how "thirsty"
a tree is, what its water potential/ efficiency/stress is. His claims
were that "it is not a trivial thing to convert something into
numbers," that the process itself is not a natural one, that we don't
know enough about it. We can use certain sets of mathematical tools
to measure certain things, and there are different kinds of math:
some of it "continuous," using real numbers, some "discontinuous,"
measurable in integers. There are also important distinctions to be
made between "amount" and "numbers"; certain phenomena are simpler to
describe on a linear curve. Is one sort of scale more "real" than
another? Because more precise? Is an account more "real" if it
provides more information? How
do we limit our understanding, if we confine ourselves to upside-down
variables, to a polarity of traits? (Does "twice as close" mean "1/2 as
far"?) What you choose to call something, how you choose to name
or measure it, is non-obvious.
During the discussion which followed, the possibilities of
"qualitative" rather than "quantitative" science were explored--as
well as the observation that, since both involve a "reduction," they
are not qualitatively different. Since Newtonian physics proved so
effective in describing the world, it has been assumed that "the more
math is used, the more serious and reputable the science is." But
what science can do is not dependent on available mathematical tools:
"you can do important science without numbers" (neither Darwin nor
Einstein originally elaborated their theories quantitatively, although
they were later tested using numbers).
The more complex a system is, the more difficult it is to minimize
it. We want a succinct language in order to be able to explore models
and generate new questions; we write theories so that numbers can be
poured into them and then manipulated. Measurement is useful in the
humanities as well as the sciences; literary critics (once) valued,
for instance, the ability to measure the abstract, musical quality of
a metrical lines. Can we imagine other ways of making sense of the
world that do not use numbers-- for instance, in terms of primal
shapes? There are many forms of categories ; a number is thought to
be a particularly precise form of measurement, but like all
abstractions, it always leaves out something.
The interface between narrative and mathematics in the social
sciences was then discussed; looking at the use of a certain word
(like "community") in documents about life at Bryn Mawr, in comparison
with its frequency of appearance in a table of "English"
language word usage, tells something about the value it is given here.
But how useful are such numbers? Sociology
synthesizes individual observations, and studies sample populations,
in order to assert something both about variability and the nature of
collective stories. What predictive value do such categories have?
Is it the notion of predictability which distinguishes a
"measurement" from a simple "category"? It was suggested that a "category," per se, has "no
predictive value"--unless one believes in first principles, assumes
an "epicenter" from which its boundaries are measured. Would it be
accurate to say that using the scientific method involves working in
categories to elaborate relations AND to predict further relations,
further elaborations? Is that the value of a poll?
Distinctions were drawn again, in conclusion, between continuous and
discontinuous measurement, between number and measurement, between mathematics and quantification. An X/Y graph only allows us to ask certain questions; rich new types of
mathematics are evolving to address new questions, new tools designed
to address problems not addressable by the old ones.
The discussion of the relationship between number and narrative will
continue next Monday @ noon, in a conversation led by Anne Dalke of
the English Department and Gender Studies Program.
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