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So this chapter deals with probably
the core problem that most

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people face when they're wrestling with
how to represent high dimensional data.

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And they have to decide what
mapping they would like to make.

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And finding the appropriate mapping
is probably the hardest part of

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doing any visualization well.

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So one of the things that I think
helps people make good decisions is to

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increase your literacy in the full
scale of possible dimensional mappings.

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So this chapter is really going to be

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high speed walk through
a number of visual mappings.

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Focusing on a few that I think
are particularly effective.

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So the first is this
idea of small multiples.

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Small multiples is a name that Tufte gives
to a technique that's been around for

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hundreds of years.

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And he describes them as postage
size postage-stamp size graphics,

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indexed by some kind of category or label.

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And they're sequenced over time,
like the frames of a movie.

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And they're ordered by some sort of
quantitative variable that's not part of

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the image itself.

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And what's key to small
multiples is this idea that we

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have a repetition of form
with a uniform presentation.

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And this allows us to focus on
the differences in the images.

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So if you look here at this very,
very wonderful early

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example of small multiple which
comes from Galileo's notebooks and

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I'm taking this particular example
from Tufte visually and he describes.

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How Galileo shows Jupiter and

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the moons of Jupiter that
are visible on consecutive nights.

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And what you see here is the organizing
principle is a vertical axis,

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that here represents time.

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But what you're able to see is that
consecutively, on different nights,

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moons appear in different
locations relative to the planet.

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And this presentation allows
you to focus immediately on

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the differences between each
of the individual knights.

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And you'll see this is used again and
again in Science.

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Here is an example showing measures
of atmospheric contaminants.

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Within the Los Angeles area.

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And what you see here is that actually
the small multiple is organized into

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three rows.

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So we've taken a nominal variable
which includes the pollutant type and

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allowed that to represent each of
the different that's shown on each row.

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And then time on the x axis, and so

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what you can see is something like
nitrogen oxide peaks very late,

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while something like hydro
carbons are peaking, are not

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active between midnight to three, but very
active throughout the rest of the day.

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So that the beauty of small multiples is
that this unique form of presentation

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allows you to quickly jump with your
eye between different iterations and

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you focus on the differences
between each of the different,

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each of the different measurements.

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So you can look at this example of
trilogies, movie trilogies represented as,

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excuse me, small multiples.

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And what you can see
here is that each set of

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trilogies is shown next to one
another with a little bar graph.

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That represents the person's
opinion of the different movies.

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And so you can see that the person
found Mad Max two to be

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even better than Mad Max one.

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Whereas if you look across Star Wars
they all seem to be fantastic.

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Whereas Jaws one was incredible and
two and three were eh,.

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Small multiples gives you a wonderful
way to compare to present this data.

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Now this data could be easily shown
in a histogram, or a line graph, but

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the small multiple representation
allows you to cluster each of

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the different variants together, and
allows you to focus on their differences.

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Here's another wonderful
example of a small multiple.

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It's lipsticks shown by an artist,
Stacy Green.

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And what's wonderful about this set
of small multiples, is saying well,

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where is the data here?

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Well, each part of these
lipsticks is a lipstick taken from

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a different woman that,
that the artist knows.

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And what you actually see is a portrait
of the woman applying the lipstick.

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And so what you get to see is the way that
they move their hand through space as

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they apply the lipstick.

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And you see that the woman in the middle.

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Really applies this twisting motion
as she applies the lipstick.

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Whereas the woman on the top middle pushes
much harder on the bottom than top as she

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moves through her So what's beautiful
about this small multiple is that you see.

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Real comparisons between each of these
unique portraits of a person, but

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the actual data is hiding
behind the image itself.

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Here's another wonderful
example of a small multiple.

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Artists has taken the covers
of Playboy magazine

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from the 60s, 70s, 80s and
90s from left to right.

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And through a technique called image
averaging has averaged all the different

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images through the centerfold and
what you can see is a true trend.

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In the male historical gaze,

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as a preference towards a going from more

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of a dark haired woman,
to a blonde haired woman.

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From more of a robust woman
to a more skinny woman.

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If we turn to a slightly more empirical
data set, let's take a look at various

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ways one might compare Fisher's Historical
data on different types of Irises.

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So perhaps I think easiest to see is this.

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Parallel plot.

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And what you see here is that each
of the different dimensions a color

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is used to represent each of the different
nominal iris categories, or types.

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And then an axis, a vertical axis,

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is used to represent each of
the different features of each category.

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And so you can see simple lengths.

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Petal length are all
represented on this scale.

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And then,
each iris is represented as a single line

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drawn across from axis to axis.

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And you can see that iris setosa
clearly clusters in the bottom left and

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has, generally has a smaller petal length.

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Then then the other irises,
like the virginica,

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which has a much larger petal length.

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So one additional,
very powerful technique for

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representing data is something
that Tufte calls a spark line.

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And it's a very small,
simple word-sized graphic.

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And Tufte describes it as having
a typographic resolution.

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And what he means is these are graphics
that we can embed into the very text of

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our scientific documents.

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And so if you have a number here,
for example, glucose at a level 6.6.

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Well, in general for
many readers this number.

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Might have no context,
or scale, or history.

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So, we can change this inline in the
document by adding a very small line graph

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that would show the data values 6.6, and
comparing it to earlier measurements.

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So, you what can see now,
is that same number.

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Actually has a history and can show
you that for this particular person

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there was a peak at a, at some
point halfway through that history.

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And it's now more at normal levels.

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Another thing that one might be
able to do, is to tie that number.

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The number which we're
describing in the text

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to the actual line graph
using a color marker.

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So, you can see that semantically we've
created a relationship between 6.6 and

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the right-most number in the line graph.

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Another additional thing
that you can do for

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a spark line is to show something that
includes the normal distribution.

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And so by you using a slightly
different background color.

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What you're now additionally
able to see is not just that

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6.6 is the latest value, but
it's within normal range.

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And that, that peak value was only above
normal range for a short period of time.

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So, the graphic itself can be
moved on either side of the.

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The actual word it's describing,
or the number,

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and that they can be embedded right
into the text of a scientific document.

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Separately, very often we find that
these types of graphs are used

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in things like,
financial pages to describe a history