Langren {HistData} | R Documentation |
Michael Florent van Langren (1598-1675) was a Dutch mathematician and astronomer, who served as a royal mathematician to King Phillip IV of Spain, and who worked on one of the most significant problems of his time— the accurate determination of longitude, particularly for navigation at sea.
In order to convince the Spanish court of the seriousness of the problem (often resulting in great losses through ship wrecks), he prepared a 1-dimensional line graph, showing all the available estimates of the distance in longitude between Toledo and Rome, which showed large errors, for even this modest distance. This 1D line graph, from Langren (1644), is believed to be the first known graph of statistical data (Friendly etal., 2009). It provides a compelling example of the notions of statistical variability and bias.
The data frame Langren1644
gives the estimates and other information derived from the
previously known 1644 graph.
It turns out that van Langren produced other versions of this graph, as early as 1628.
The data frame Langren.all
gives the estimates derived
from all known versions of this graph.
data(Langren1644) data(Langren.all)
Langren1644
: A data frame with 12 observations on the following 5 variables,
giving determinations of the distance in longitude between Toledo and Rome, from the 1644 graph.
Name
A. Argelius
... T. Brahe
Longitude
Year
Longname
Name
, where appropriate; a factor with levels Andrea Argoli
Christoph Clavius
Tycho Brahe
Where
Alexandria
Belgium
Denmark
Flanders
France
Germany
Italy
Italy
Langren.all
: A data frame with 61 observations on the following 4 variables,
giving determinations of Longitude between Toledo and Rome from all known versions of van Langren's graph.
Author
Langren
Lelewel
Year
Name
Algunos1
Algunos2
Apianus
... Schonerus
Longitude
In all the graphs, Toledo is implicitly at the origin and Rome is located relatively at the value of Longitude
To judge correspondence with an actual map, the positions in (lat, long) are
toledo <- c(39.86, -4.03);
rome <- c(41.89, 12.5)
The longitude values were digitized from images of the various graphs, which may be found on the Supplementary materials page for Friendly etal. (2009).
Friendly, M., Valero-Mora, P. and Ulargui, J. I. (2009). The First (Known) Statistical Graph: Michael Florent van Langren and the "Secret" of Longitude. Unpublished ms (submitted). Supplementary materials: http://www.math.yorku.ca/SCS/Gallery/langren/.
Langren, M. F. van. (1644). La Verdadera Longitud por Mar y Tierra. Antwerp: (n.p.), 1644. English translation available at http://www.math.yorku.ca/SCS/Gallery/langren/verdadera.pdf.
Lelewel, J. (1851). Géographie du Moyen Âge. Paris: Pilliet, 1851.
data(Langren1644) ## Not run: require(maps) require(ggplot2) require(reshape) require(plyr) # set latitude to that of Toledo Langren1644$Latitude <- 39.68 # x/long y/lat bbox <- c( 38.186, -9.184, 43.692, 28.674 ) bbox <- matrix(bbox, 2, 2, byrow=TRUE) borders <- as.data.frame(map("world", plot = FALSE, xlim = expand_range(bbox[,2], 0.2), ylim = expand_range(bbox[,1], 0.2))[c("x", "y")]) data(world.cities) # get actual locations of Toledo & Rome cities <- subset(world.cities, name %in% c("Rome", "Toledo") & country.etc %in% c("Spain", "Italy")) colnames(cities)[4:5]<-c("Latitude", "Longitude") mplot <- ggplot(Langren1644, aes(Longitude, Latitude) ) + geom_path(aes(x, y), borders, colour = "grey60") + geom_point(y = 40) + geom_text(aes(label = Name), y = 40.1, angle = 90, hjust = 0, size = 3) mplot <- mplot + geom_segment(aes(x=-4.03, y=40, xend=30, yend=40)) mplot <- mplot + geom_point(data = cities, colour = "red", size = 2) + geom_text(data=cities, aes(label=name), color="red", size=3, vjust=-0.5) + coord_cartesian(xlim=bbox[,2], ylim=bbox[,1]) # make the plot have approximately aspect ratio = 1 windows(width=10, height=2) mplot ## End(Not run) if (require(ReadImages)) { gimage <- read.jpeg(system.file("images", "google-toledo-rome3.jpg", package="HistData")) plot(gimage) # pixel coordinates of Toledo and Rome in the image, measured from the bottom left corner toledo.map <- c(130, 59) rome.map <- c(505, 119) # confirm locations of Toledo and Rome points(rbind(toledo.map, rome.map), cex=2) # set a scale for translation of lat,long to pixel x,y scale <- data.frame(x=c(130, 856), y=c(52,52)) rownames(scale)=c(0,30) lines(scale) xlate <- function(x) { 130+x*726/30 } points(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), pch=25, col="blue") text(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), labels=Langren1644$Name, srt=90, adj=c(0, 0.5), cex=0.8) } # show variation in estimates across graphs library(lattice) graph <- paste(Langren.all$Author, Langren.all$Year) dotplot(Name ~ Longitude, data=Langren.all) dotplot( as.factor(Year) ~ Longitude, data=Langren.all, groups=Name) dotplot(Name ~ Longitude|graph, data=Langren.all, groups=graph)