So this chapter deals with probably
the core problem that most
people face when they're wrestling with
how to represent high dimensional data.
And they have to decide what
mapping they would like to make.
And finding the appropriate mapping
is probably the hardest part of
doing any visualization well.
So one of the things that I think
helps people make good decisions is to
increase your literacy in the full
scale of possible dimensional mappings.
So this chapter is really going to be
high speed walk through
a number of visual mappings.
Focusing on a few that I think
are particularly effective.
So the first is this
idea of small multiples.
Small multiples is a name that Tufte gives
to a technique that's been around for
hundreds of years.
And he describes them as postage
size postage-stamp size graphics,
indexed by some kind of category or label.
And they're sequenced over time,
like the frames of a movie.
And they're ordered by some sort of
quantitative variable that's not part of
the image itself.
And what's key to small
multiples is this idea that we
have a repetition of form
with a uniform presentation.
And this allows us to focus on
the differences in the images.
So if you look here at this very,
very wonderful early
example of small multiple which
comes from Galileo's notebooks and
I'm taking this particular example
from Tufte visually and he describes.
How Galileo shows Jupiter and
the moons of Jupiter that
are visible on consecutive nights.
And what you see here is the organizing
principle is a vertical axis,
that here represents time.
But what you're able to see is that
consecutively, on different nights,
moons appear in different
locations relative to the planet.
And this presentation allows
you to focus immediately on
the differences between each
of the individual knights.
And you'll see this is used again and
again in Science.
Here is an example showing measures
of atmospheric contaminants.
Within the Los Angeles area.
And what you see here is that actually
the small multiple is organized into
three rows.
So we've taken a nominal variable
which includes the pollutant type and
allowed that to represent each of
the different that's shown on each row.
And then time on the x axis, and so
what you can see is something like
nitrogen oxide peaks very late,
while something like hydro
carbons are peaking, are not
active between midnight to three, but very
active throughout the rest of the day.
So that the beauty of small multiples is
that this unique form of presentation
allows you to quickly jump with your
eye between different iterations and
you focus on the differences
between each of the different,
each of the different measurements.
So you can look at this example of
trilogies, movie trilogies represented as,
excuse me, small multiples.
And what you can see
here is that each set of
trilogies is shown next to one
another with a little bar graph.
That represents the person's
opinion of the different movies.
And so you can see that the person
found Mad Max two to be
even better than Mad Max one.
Whereas if you look across Star Wars
they all seem to be fantastic.
Whereas Jaws one was incredible and
two and three were eh,.
Small multiples gives you a wonderful
way to compare to present this data.
Now this data could be easily shown
in a histogram, or a line graph, but
the small multiple representation
allows you to cluster each of
the different variants together, and
allows you to focus on their differences.
Here's another wonderful
example of a small multiple.
It's lipsticks shown by an artist,
Stacy Green.
And what's wonderful about this set
of small multiples, is saying well,
where is the data here?
Well, each part of these
lipsticks is a lipstick taken from
a different woman that,
that the artist knows.
And what you actually see is a portrait
of the woman applying the lipstick.
And so what you get to see is the way that
they move their hand through space as
they apply the lipstick.
And you see that the woman in the middle.
Really applies this twisting motion
as she applies the lipstick.
Whereas the woman on the top middle pushes
much harder on the bottom than top as she
moves through her So what's beautiful
about this small multiple is that you see.
Real comparisons between each of these
unique portraits of a person, but
the actual data is hiding
behind the image itself.
Here's another wonderful
example of a small multiple.
Artists has taken the covers
of Playboy magazine
from the 60s, 70s, 80s and
90s from left to right.
And through a technique called image
averaging has averaged all the different
images through the centerfold and
what you can see is a true trend.
In the male historical gaze,
as a preference towards a going from more
of a dark haired woman,
to a blonde haired woman.
From more of a robust woman
to a more skinny woman.
If we turn to a slightly more empirical
data set, let's take a look at various
ways one might compare Fisher's Historical
data on different types of Irises.
So perhaps I think easiest to see is this.
Parallel plot.
And what you see here is that each
of the different dimensions a color
is used to represent each of the different
nominal iris categories, or types.
And then an axis, a vertical axis,
is used to represent each of
the different features of each category.
And so you can see simple lengths.
Petal length are all
represented on this scale.
And then,
each iris is represented as a single line
drawn across from axis to axis.
And you can see that iris setosa
clearly clusters in the bottom left and
has, generally has a smaller petal length.
Then then the other irises,
like the virginica,
which has a much larger petal length.
So one additional,
very powerful technique for
representing data is something
that Tufte calls a spark line.
And it's a very small,
simple word-sized graphic.
And Tufte describes it as having
a typographic resolution.
And what he means is these are graphics
that we can embed into the very text of
our scientific documents.
And so if you have a number here,
for example, glucose at a level 6.6.
Well, in general for
many readers this number.
Might have no context,
or scale, or history.
So, we can change this inline in the
document by adding a very small line graph
that would show the data values 6.6, and
comparing it to earlier measurements.
So, you what can see now,
is that same number.
Actually has a history and can show
you that for this particular person
there was a peak at a, at some
point halfway through that history.
And it's now more at normal levels.
Another thing that one might be
able to do, is to tie that number.
The number which we're
describing in the text
to the actual line graph
using a color marker.
So, you can see that semantically we've
created a relationship between 6.6 and
the right-most number in the line graph.
Another additional thing
that you can do for
a spark line is to show something that
includes the normal distribution.
And so by you using a slightly
different background color.
What you're now additionally
able to see is not just that
6.6 is the latest value, but
it's within normal range.
And that, that peak value was only above
normal range for a short period of time.
So, the graphic itself can be
moved on either side of the.
The actual word it's describing,
or the number,
and that they can be embedded right
into the text of a scientific document.
Separately, very often we find that
these types of graphs are used
in things like,
financial pages to describe a history