Taming the Dimensions-Visualizations in Science, Filozofia, Filozofia - Artykuły
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Philosophy of Science Association
Taming the Dimensions-Visualizations in Science
Author(s): William C. Wimsatt
Source: PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association,
Vol. 1990, Volume Two: Symposia and Invited Papers (1990), pp. 111-135
Published by: The University of Chicago Press on behalf of the Philosophy of Science
Association
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PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.
Taming
the Dimensions-Visualizations in Science1
William C. Wimsatt
The
University
of
Chicago
The
role of
pictures
and visual
modes of
presentation
of data in science is a
topic
of
increasing
interest to workers in artificial
intelligence,
the
psychology
of
problem
solving,
and
increasing
numbersof scientists in all fields who must deal with
prob-
lems of how to
representlarge quantities
of
complex
multidimensional data in an in-
telligible
fashion.
The
use
of
pictures
is
marvelously
illustrated
by
but not limited to
the
biological sciences,
so
I will
use
examples
from elsewhere as
appropriate.
With
the
development
of our visual
technology-television, videotape,
and the
computer,
the uses
(and misuses)
of visualization has
properly
become a matternot
only
of theo-
retical but also of
practical
concer. I will startwith a
practical story
because it has
multiple
morals,
both
practical
and theoretical-most of which lead elsewhere than I
wish to
go
here.
A
colleague
of
mine,
J. Z.
Smith,
got
into a discussion about
pictures
with his
freshman humanities class. Whereas we academics trustand
pay
close attentionto the
written
word,
and find visualization
mysterious
and more than a little
suspicious,
he
was
quite
astoundedto find out that their characteristicreaction was
quite
the reverse.
The
evening "Eyewitness
News",
because
pictured-often
"live"
by portable
video-
cam-was to them irrefutableand
trustworthy,
whereas
(partlythrough
our
efforts)
they
were
quite
awareof the means of
manipulating
the written
word,
and thus much
more
suspicious
of it. Smith's
message
was that we academics
spend
all of our time
telling
our studentshow to read
critically
and
suspiciously,
but
ignore
the information
channel from which
they get
most information-which to
them
is
also
the
most
real
and reliable.
(Similarly
BrunoLatour
(1987)
comments that data
presented
in
graphic
format seems "morereal"thanthe numbersfrom which the
graph
was
drawn.)
This
should all seem
quite surprizing
and anomalousto most of us-it did to me.
Smith was able to make a deal with an audio-visual
teacher at a local
college (we
don't have such
things
at
my university,
of
course!)
to
tape
a
meeting
of his class and
edit it down to one
minute,
as if it were
going
on the
nightly
news. The A-V teacher
was
delighted
-the
taping
and
editing
became a
project
for
his class.
They
did an ex-
cellent
job.
But when Smith's class saw the finished
result,
they
were
outraged.
Class
incidents were
collapsed,
taken out of
context,
and even
permuted (so
that a stu-
PSA
1990,
Volume
2,
pp.
111-135
Copyright
? 1991
by
the
Philosophy
of Science Association
112
dent's
question
was "answered"
by
another's
remark
given
earlier
in
response
to an-
other
question).
The students
got
a new
respect
for the foibles of the media.
But this is not the issue of
my paper.
Nor is this a
good example
to startan
analysis
with-it is too
real,
messy,
and uncontrolled. It makes
nicely
the
point
of the
ubiquity,
immediacy,
and
supposedreliability
of
visualizations,
but it doesn't
suggest why.
The
promising
issue of
biases induced
by
visualizations
in
the
presentation
of data
(an
im-
portanttopic-see
Tufte
(1983, 1990))
are in this case confoundedwith too
many
bio-
logical
(sensory), psychological (cognitive
and
affective),
and social
(economic,
cultur-
al,
and
ideological)
variables. It is a
good
case to
keep
in mind
however,
in
response
to
questions
like:
"Why
work on
pictures?
Aren't words
(or
equations)
all that
really
count?" As Mike Ruse
points
out in his
contribution,
a
surprizinglylarge proportion
of
scientists' work is devoted to
taking,making,designing,
and
evaluatingpictures.
(See
also
Lynch
and
Woolgar 1990).
There are
things
which are at least
virtuallyimpossible
(to
scientists or
engineers,
I
would
say impossible,
but
philosophers
would misunder-
stand
that)
to do without
visualization,
and-whether
possible
or not-no-one in their
right
mind would
try
to do so. These are
usually
also
things
thatvisualization is best
suited for.
For
pragmaticreasons,
I will
only sample
these
in a
biased
fashion: I have
not the
space,
nor the facilities
(color,
high
resolution
graphics,
motion
pictures,
or
stereoscopic presentation)
to do more. I will instead discuss
(andillustrate)
some of
my
favorite
issues,
focussing
on robustnessand multidimensional
complexity.
Part of
my message
with these
examples
is that in
using pictures,
we are for
many
problems giving
the most
natural,
economical,
and
inferentially
fruitful
representa-
tions of data. To the extent that theories aim to
organize
and
simplify
(in
their role as
templates
for
organizing
data for
analysis), pictures
can have a
theory-like
status. (It
would be
tempting
to
say
that
they
are in that
respect propositional-but
that biases
the
case
just
as
strongly
as
if I
said
thatall
propositions
were
picture-like).
Even if
something
is in
principle representable
in another
way (conceivable,
or even
plausible
if we
place
no constraintson
complexity)
we should be interestedin
finding
the most
naturaland
simplest ways
of
representing
the informationand structureof a
prob-
lem-usually
thus
aiding
both its robust
understanding
and its solution. This solution
is often visual.
If
something
is
easier,
we will do it that
way by
choice,
or-in a race of different
methods
against
time--do it that
way
first.
Getting
there first is
important
in evolu-
tion,
and indeed in all selection
processes. Biologists
are often
asked,
if it is
so
easy
to make
life,
why
isn't it
happening
all of the time? The standardanswer is that it
probably
is,
but it is
getting
eaten
immediately by
those who
got
there first.
(See
Simon
(1981),
ch. 7 for a more
serious
argumentalong
the same
lines.)
Another vari-
ant of the same
point
is the observation
that,
once
invented,
it is easier to
modify
a
method or an
adaptationoriginally designed
for different
purposes
than to construct a
new one from scratch.
(Schank
and Wimsatt
1988)).
In this
light,
it is
sobering
to real-
ize that visualization is a far older
adaptive
mode than
language.
Visual
thinking
should turn out to be far more
pervasive
than those of us raised on
"linguistic philoso-
phy"
have
given
it credit for.
1. Some
simple examples (without pictures)
Can
you
intersect a cube with a
plane
in such a
way
as to make a
regularhexagon?
Most
people say they
don't
know,
or if
pressed say
that
they
are
pretty
sure
you
can't.
(This
is
impressive
because
just asking
the
question
in this
way suggests
that the an-
swer is
surely "yes"
and
they
are
supposed
to
figure
out
how.)
This
problem
is
rapid-
ly
solved
through visualization,
but almost
impossible
without it. One also can see
113
symmetries.
A
verystrong
hintis thatthesolutionwill involve
connecting
the
midpoints
of
edges
of
thecube
(and
remember-you
needsix of
them!),
but
why
thisis a
good
hintis
not
obviousuntilone drawsthevisualsolution.
(I
don'teven
knowof a non-visualsolu-
tion,
thoughyou
could
undoubtedly
laboriously
constructone
by working
backwards
fromthe solutionwithan
analytical
(though
still
geometric)
proof.
I won'tshow
you
this
picture-you
shoulddiscoverit
yourself
to feel theforceof thevisualsolution.
Drawthe
cube,
andthen
try
thehint.
Problem-solving
often
requires
visualization,
butso alsodoes
patternrecognition
anddiscrimination.
Indeed,
thisis
probably
serving
directedlocomotion
surely
cameearlierin
simplersystems
whichcould
only
tell
light
from
dark,
andthus
couldnotdiscriminate
patterns.)
EdwardTufte
(1983)opens
his landmark
book,The
Visual
Displayof
Quantitative
Information,
withan
example
dueto statisticianF.J.
Anscombe.
Anscombe
presents
4 datasetsof 11
pairs
of
points,
eachof whichfit the
samelinearmodel
equally
(and
tolerably)
well. Onecannottell
by looking
atthetab-
ulateddatasetsthatone is a
typicalregression
lineof moderate
slope
with
good
Gaussian
scatter,
one is an
absolutelystraightregression
linewithno scattersavefor
one severe
outlier,
one is a beautifulbut
assymmetricpart
of a
parabola,
andone is a
degenerate
case of a verticalline
(no
variation
in the
independentvariable)
withan
outlier.Whichcase
applies
is of course
veryimportant
both
forcausalinferenceand
for
judging
the
quality
of thedata.
Anscombe's
point
was to showthat
only
a fool
depends
on statistical
analysis
alonewithoutever
literallylooking
atthe
data,but
the
case is a
set-up-a trap-in
a
revealingway.
It is normal
(at
least
for
experimentaldata,
wherevaluesare
usually
producedby systematicallychanging
thevaluesof the
independent
variable)
to
pre-
sentthedataordered
by
monotonicincreasesin the
independent
in this
way,
one
can
immediately
"see"thedif-
ferent
character
of
thefoursetsof data,and"readoff' the
graphs
fromthetablesof
numbers.It is
tempting
to
say
thatAnscombe's
(abnormal)procedure
showsthatwe
don't
really
needto
look atthedataif we
present
it
right.
Butthisis a
double-edged
sword. It
just
as
stronglysupports
theconclusionthatwe have
internalizedvisual
constraints
(x)
variable.If
the
data! Notethatthestatisticsdo
notdiscriminate
amongdifferent
orders
for
presenting
he
data,
so therewouldbe no
analyticalhelp
in
telling
us thatwe shouldorderourdatain this
way. (Indeed
order-
independence
would
surely
be held
up
as a
necessary
conditionfor
any
usefulstatisti-
cal measures.
Thingsget veryembarrassing
(Wimsatt
1985)).Storage
and
analysis
of
multi-componentquantitative
datain termsof
systematic(monotonic)
change
of
important
variablesis a characteristic
spatial
order.2This
is truewhetherthedatais
presented
-and
characteristically
in
analytical
ortabularformor in
visual2- or 3-dimensional
space.
2.
Picturing
multidimensional
complexities
using
heuristicsof thevisual
system
data
is now a "hot"
topic.
2 and
3-spaces
sound
very
limiting
in thesetimesof
multiple
re-
gressions
withhundredsof variables.
Wecan't
go
to several
hundred,
butwe cando a
lot betterthan2 or 3
by utilizing
other
discriminatory
of
multi-component
(more
commonly,"multi-dimensional")
powers
of thevisual
system.
It
is
veryeasy
with
color,
variationin size or
intensity
of
symbols,
and
temporal
"slic-
ing",
to
represent
4
to 6
components
ordimensions
in a 2-D
representation
of a
3-
(withthe
picture,
butnot
before)
thatthisconstruction
requires
a cube-a
rectangular
parallelpiped
will notdo-and thatthesolutionhas
unanticipated
themostbasicskillforwhichthe
more
complex
visual
systems
were
designed.(Orientation
Anscombe'sdata-setsare
rearranged
in ournormalmannerof
presenting
fordata
analysts
if datahaveto be
pre-
sentedin a certain
order-statisticsmustbe
"aggregates"
of
representing
visual-way
Representation
Figure
1:
The
use of "small
multiples"(with
a
geographicalkey) permitscompactrepresentation
of multidimensionaldatain a formatwhichis not
confusing.
Here
changing
concentrationsof three
components
of airborne
pollution
in Los
Angeles
are
graphed
over
space
andtime-4 dimensionsof data. Los
Angeles
Times,January22, 1979,
basedon workof
Gregory
J. MacRae,CaliforniaInstituteof
Technology,reprinted
from
Tufte
1983,
p.
42.
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