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CHANCE
53
[Visual Revelations]
Howard Wainer
Column Editor
Stigler’s law of eponymy: No scientific discovery is
named after its original discoverer.1
In the 1878 edition of his book La Méthode
Graphique dans les Sciences Expérimentales et Particuliére-
ment en Physiologie et en Médecine, Fren ch sc ie nti st E. J.
Marey (1830–1904) reproduced a marvelous graphic
train schedule whose design he attributed to Ibry (see
Figure 1). e vertical axis is geographic, showing the
train stations between Paris and Lyon spaced propor-
tional to their physical distance. e horizontal axis
represents one day of time spaced in one-hour inter-
vals. Drawn on this framework are slanted lines that
represent trains. Trains from the top left to the bottom
right are those going from Paris to Lyon; those with
the opposite slope go from Lyon to Paris. Faster trains
have a steeper slope. An entire train schedule can be
seen and understood in a glance.
This display design has received well-deserved
and widespread accolades. Edward Tufte thought so
highly of the design that he included it on the cover
of his iconic book, e Visual Display of Quantitative
Information, and used the same design to represent
trains between New York City and Hoboken. Howard
Wain er, i n Visual Revelations: Graphical Tales of Fate
Figure 1. A French train schedule designed by Ibry and published in Paris by Marey in 1878
Stigler’s Law of Eponymy
and Marey’s Train Schedule
Did Serjev Do It Before Ibry, and What
About Jules Petiet?
Howard Wainer, Polina Harik, and John Neter
1 Stephen Stigler named the sociologist Robert K. Merton as the discoverer of “Stigler’s law”
VOL. 26.1, 2013
54
and Deception from Napoleon Bonaparte to Ross Perot,
showed how this design could illuminate the bus service
in Los Angeles.
Was Ibry the rst to use this design? Were the Rus-
sians there earlier?
During a visit to Moscow in 1993, Bart Bielawski—
an American engineer of Polish descent—was
approached on the street by a Russian who told him
of a remarkable old chart he had in his possession. He
asked Bielawski if he would be interested in purchasing
it. e chart in question was printed in St. Petersburg
in May of 1854 and, among other things, incudes a
graphical train schedule closely akin to Ibry’s design,
showing both passenger and freight trains between
Moscow and St. Petersburg. e display declares it
was “created by Second Lieutenant Serjev, who was a
member of the Corps of Transportation Engineers.”
e chart is shown as Figure 2 and is comprised
of three main panels. e top panel is a map of Russia
showing the 600 kilometers of train tracks between St.
Petersburg on the west and Moscow on the east. In
addition to the distance, it also contains the altitude.
Such information is of obvious importance to railroad
engineers. It is amusing to note the local bias, in that
the altitudes are given as the distance above sea level,
but not the level of just any sea; it is above the level of
the Baltic.
Below the map are two other panels. e larger
one is of principal historic interest, for it is a graphic
train schedule that predates Ibry’s by as much as 24
years and, although it is practically identical to Ibry’s,
it rests within a much richer environment. e vertical
axis, as in Ibry’s design, is geographic, representing the
600 kilometers (and 35 railway stations) between St.
Petersburg on the top and Moscow on the bottom,
spaced approximately proportional to the geographic
distances. e horizontal axis represents time. e
bottom axis goes from 1 to 12 and then repeats itself
almost ve times, representing almost two-and-a-half
days. e top axis is divided into four categories: Night
12 to 6, Morning 7 to 12, Day 1 to 6, and Evening 7 to
12. e categories are then repeated. e lines drawn on
Figure 2. An augmented graphic train schedule designed by Serjev and published in St. Petersburg in May of 1854
CHANCE
55
the chart represent the locations of trains. e red lines
with a negative slope represent passenger trains going
from St. Petersburg to Moscow; those with a positive
slope, colored blue, are passenger trains that go from
Moscow to St. Petersburg. Black lines are reserved for
freight trains. It is apparent at a glance that steeper lines
represent faster trains.
Note that the fastest train leaves St. Petersburg at 11
in the morning and doesn’t arrive in Moscow until 9 the
following morning—a voyage of 22 hours. No wonder
Serjev designed his schedule to cover two-and-a-half
times the length of time that Ibry did in his. It is not
solely because Russia is a vastly larger country than
France, although that is surely part of the story, but
because Russian trains were a lot slower. e slowest
trains over that distance took fully two days!
e table on the bottom right provides taris for
freight. e accompanying narrative indicates that
freight fees were based on value of the product, and
not solely on weight or size. Sometimes prices are in
kopeks, sometimes in “silver rubles.”
Figure 3. A graphic train schedule of BART trains (downloaded from www.drones.com/bart.html on August 22, 2012)
We note, in passing, that train schedules are now
often prepared using Serjev’s design, but typically
they lack the richness of additional material that
provides context. One example, chosen more-or-less
at random, is shown in Figure 3. It shows the trains
of the Bay Area Rapid Transit (BART) system. Of
course, we can summarize what is contained in the
schedule by simply noting that BART trains come
every few minutes, so, except in the wee small hours,
just show up. A line of prose could have substituted
for the graphic eciently and accurately.
ere is no parallel simplication that would work
for either Ibry’s French display or Serjev’s marvelous
Russian one.
A worthy companion to Ibry’s and Serjev’s designs
was produced in November 1937 showing the Java
railroad line between Socrabaja and Djokjakarta,
which includes a prole of the topography of the land,
as well as the trains and their schedules. A high-qual-
ity reproduction of this display with an accompanying
discussion is found in Tufte’s Envisioning Information.
VOL. 26.1, 2013
56
About the Author
Howard Wainer is currently distinguished research
scientist at the National Board of Medical Examiners and
professor of statistics at the Wharton School, University of
Pennsylvania. He has won numerous awards and is a Fellow
of the American Statistical Association and the American
Educational Research Association. His interests include the use
of graphical methods for data analysis and communication,
robust statistical methodology, and the development and
application of generalizations of item response theory. He
has published many books; his latest is Uneducated Guesses:
Using Evidence to Uncover Misguided Education Policies.
Coda
e graphic train schedule has long been associated
with the name of Étienne-Jules Marey, even though
its original designer, Ibry, has been prominently
mentioned (see The Visual Display of Quantitative
Information). We should have suspected, from Stigler’s
Law, that there was an earlier progenitor still. Could
it be the mysterious Second Lieutenant Serjev? Tufte
(email 8/22/12) suggested that Serjev’s display “looks
quite polished so there (likely) were others before,
probably internal railroad planning schedules.” Indeed,
it is hard to believe that the 1854 display was the rst
attempt. Were there earlier attempts? If so, how much
earlier? And by who?
Yet the same observation could be made about Ibry’s
design. Was it also more polished than we would expect
from an initial eort? Stephen Stigler (email 8/22/12)
pointed us to an 1884 article by Leon Lalanne in which
he carefully describes the Ibry design. He explains
that it is such an evocative means of displaying the
operations of train networks that it has been put into
place throughout France’s rail system. He believes its
adoption took place as a direct consequence of a ter-
rible rail accident that occurred on May 8, 1842, on the
Versailles train. He dates the rst such display from a
memoire, “Tracé géométrique de la marche et de la
composition des trains,”2 by someone he identies as
“a skillful engineer, Jules Petiet, who later became chief
operating ocer of the Northern Railway.” e design
of the new train schedule was apparently contained in
that memoir. According to Lalanne’s description, the
width of the lines representing the trains was propor-
tional to the number of cars. Such an embellishment
moves this display in the direction of the ow maps
later made famous by Minard.
Lalanne also sheds some light on the identity of
the almost anonymous Ibry. He reports that “Mr. Ibry,
deputy chief operating ocer of the railway from
Paris to Rouen, after using these kinds of displays for
several years at the end of 1846, arranged, with the
encouragement of the administration and public works
corporation to have these gures produced widely. is
action received a very favorable reaction.” Precursors to
Ibry’s design are also found in Lalanne’s 1845 report
on weather maps.
Which brings us back to eponymy. “Marey’s train
schedule” is surely wrong, although that is how such
designs are most commonly known. Would it be better
to call them Ibry’s? Or Serjev’s? To our knowledge, they
have never been referred to as “Petiet’s train schedules”
and so, by Stigler’s Law, he has a fair shot as its origina-
tor, but where and when did Serjev get the idea?
Further Reading
Marey, E. J. 1878. La Méthode graphique dans les sciences
expérimentales et particuliérement en physiologie et en
médecine. P aris.
Lalanne, L. 1845. Sur la representation graphique des
tableaux météorlogiques et des lois naturelles en
general. Appendix to Cours complet de météorlogie de
L. F. Kaemtz, traduit et annoté par Ch. Martins, Par is .
Lalanne, L. 1884. Methodes graphique: Note sur un
nouveau mode de representation de la march des
trains sur une voie de communication. Compte
Rendus 99:307–313.
Stigler, S. M. 1980. Stigler’s Law of Eponymy. Trans-
actions of the New York Academy of Sciences
39:147–157. Reprinted as Chapter 14 in Stigler’s
(1999) Statistics on the table. Cambridge, Mass:
Harvard University Press.
Tu ft e, E . R . 1 98 3. The visual display of quantitative
information. Graphics Press, Cheshire, CT.
Tu ft e , E . R . 19 9 0. Envisioning information. Che shire,
CT: Graphics Press.
Wain er, H. 1 99 7. Visual revelations: Graphical tales of
fate and deception from Napoleon Bonaparte to Ross
Perot. New York: Copernicus Books.
2 A geometric representation of the operation and composition of trains.
(translation by HW).