# [R] plotting on a reverse log scale

Michael Friendly friendly at yorku.ca
Thu Jul 7 20:49:40 CEST 2005

```Thanks to all who replied, particularly Duncan Murdoch, whose solution I
It thought it might be of interest to some to see the results and
compare these ways
of representing the distribution of historical events over time.
The events are the items I record on my site, Milestones in the History
of Data
Visualization,
http://www.math.yorku.ca/SCS/Gallery/milestones

Here is the subset of events post 1500:

subset<-
c(1530, 1533, 1545, 1550, 1556, 1562, 1569, 1570, 1572, 1581,
1605, 1603, 1603, 1614, 1617, 1624, 1623, 1626, 1632, 1637, 1644,
1646, 1654, 1654, 1657, 1663, 1662, 1666, 1669, 1671, 1686, 1686,
1687, 1693, 1693, 1701, 1710, 1711, 1712, 1724, 1727, 1745, 1741,
1748, 1752, 1752, 1752, 1753, 1765, 1760, 1763, 1765, 1765, 1781,
1776, 1778, 1779, 1782, 1782, 1782, 1785, 1786, 1787, 1794, 1795,
1796, 1798, 1798, 1800, 1800, 1801, 1801, 1809, 1811, 1817, 1819,
1825, 1821, 1822, 1825, 1827, 1828, 1832, 1830, 1832, 1833, 1833,
1833, 1833, 1836, 1836, 1837, 1838, 1839, 1839, 1843, 1843, 1843,
1844, 1846, 1846, 1851, 1852, 1853, 1855, 1857, 1857, 1857, 1861,
1861, 1863, 1868, 1869, 1869, 1869, 1872, 1872, 1872, 1872, 1873,
1874, 1874, 1874, 1874, 1875, 1875, 1877, 1877, 1877, 1878, 1878,
1879, 1879, 1889, 1880, 1882, 1882, 1883, 1884, 1884, 1884, 1884,
1884, 1885, 1885, 1885, 1888, 1892, 1895, 1896, 1899, 1901, 1904,
1905, 1910, 1910, 1911, 1912, 1913, 1913, 1913, 1913, 1914, 1914,
1915, 1920, 1916, 1917, 1925, 1919, 1920, 1923, 1923, 1924, 1925,
1926, 1929, 1928, 1928, 1929, 1930, 1931, 1933, 1942, 1937, 1939,
1944, 1944, 1957, 1957, 1958, 1962, 1965, 1966, 1965, 1967, 1968,
1969, 1969, 1969, 1971, 1971, 1972, 1973, 1973, 1974, 1974, 1974,
1974, 1975, 1975, 1975, 1975, 1975, 1976, 1977, 1977, 1978, 1978,
1979, 1981, 1981, 1981, 1982, 1982, 1983, 1983, 1985, 1985, 1987,
1988, 1988, 1989, 1989, 1990, 1990, 1990, 1990, 1990, 1991, 1991,
1993, 1992, 1994, 1996, 1999)
>

The standard density plot, labeled according to periods of time
shows quite interpretable trends,

#  standard plot
plot(density(subset, from=1500, to=1990, bw="sj"),
main="Milestones: Time course of development",
xlab="Year")
ref <-c(1600, 1700, 1800, 1850, 1900, 1950, 1975)
abline(v= ref, lty=3, col="blue")

labx<-c(1550, 1650, 1750, 1825, 1875, 1925, 1962, 1987)
laby<- 0.003 + 0.0003 * c(0, 1, 2, 3, 5, 3, 5, 2)
txt1 <-c("Early maps",
"Measurement\n& theory",
"New graphic\nforms",
"Modern\nage",
"Golden Age",
"Modern dark\nages",
"Re-birth",
"Hi-D Vis")
text(labx, laby, labels=txt1, cex=1.25, xpd=TRUE)
rug(subset, quiet=TRUE)

The idea of a reverse log scale for representing events in time was
suggested by
\whom{Heinz}{Von Foerster} in 1930, and this (below) produces the
corresponding
plot;  you might imagine this as a view of the density of events standing at
the year 2000, and looking back at time through a log-scaled telescope.
I wanted to see what this looked like, but I'm not sure it is of
particularly
greater use here, except to suggest alternative ways to represent historical

#  reverse log plot
rlogyear <- -log(2000-subset)

#from <- -log(2000-1990)
#to <- -log(2000-start)
# need to swap, so from < to for density
to <- -log(2000-1990)
from <- -log(2000-start)

plot(density(rlogyear, from=from, to=to, bw="sj"), axes=F,
main="Milestones: Time course of development",
xlab="Year (reverse log scale)")
rug(rlogyear, quiet=TRUE)

labels <- pretty(subset)
labels <- c(labels[labels<2000], 1950, 1975, 1990)
axis(1, labels, at=-log(2000-labels))

minorticks <- pretty(subset, n=30)
minorticks <- minorticks[minorticks<2000]
axis(1, labels=FALSE, at=-log(2000-minorticks), tcl=-0.25)
axis(2)

ref <-c(1600, 1700, 1800, 1850, 1900, 1950, 1975)
abline(v= -log(2000-ref), lty=3, col="blue")

labx<-c(1550, 1650, 1750, 1825, 1875, 1925, 1962, 1987)
laby<- 0.35 + 0.03 * c(-1, .5, 2.2, 4, 1.6, .3, -1, -2)
text(-log(2000-labx), laby, labels=txt1, cex=1.2, xpd=TRUE)
box()

Final question:
How can I reduce the interline space in multiline strings?
From ?par, I tried lheight:
> text(-log(2000-labx), laby, labels=txt1, cex=1.2, xpd=TRUE, lheight=.8)
NULL
Warning message:
parameter "lheight" couldn't be set in high-level plot() function
>

--
Michael Friendly     Email: friendly at yorku.ca
Professor, Psychology Dept.
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    http://www.math.yorku.ca/SCS/friendly.html