Ford, there is an infinite number of monkeys outside who want to talk to us about this script for Hamlet they have worked out (from Episode 2 of The Hitchhiker’s Guide to the Galaxy by Douglas Adams)
Some days ago I was talking with a friend about the infinite monkey theorem which is a funny interpretation of what thinking-in-infinite can produce. The same day, in my weekly English class, my teacher said that Anglo-saxon words do tend to be short, very often monosyllabic such as function words such as to, of, from etc and everyday words such as go, see run, eat, etc.
Both things made me think that a monkey could have easier to type a Shakespeare text rather than a Cervantes one. I cannot imagine a definitive way to demonstrate this but this experiment support my hypothesis. After simulating random words of 2, 3, 4 and 5 characters I look for them in English(1) and Spanish(2) dictionaries, which I previously downloaded from here. Result: I find more random words in the English one. These are the results of my experiment:
For example, around 38% of two-chars words match with English dictionary and only 9% with Spanish one. This is why I think that, in the infinite, I would be easier for a monkey to replicate a Shakespeare text than a Cervantes one.
Here you have the code:
library(ggplot2)
library(scales)
esp.dic=data.frame(LANG="ESP", WORD=readLines("ES.dic"))
eng.dic=data.frame(LANG="ENG", WORD=readLines("UK.dic"))
df.lang=do.call("rbind", list(esp.dic, eng.dic))
df.lang$WORD=tolower(iconv(df.lang$WORD, to="ASCII//TRANSLIT"))
df.lang=unique(df.lang)
results=data.frame(LANG=character(0), OCCURRENCES=numeric(0), SIZE=numeric(0), LENGTH=numeric(0))
for (i in 2:5)
{
df.monkey=data.frame(WORD=replicate(20000, paste(sample(c(letters), i, replace = TRUE), collapse='')))
results=rbind(results, data.frame(setNames(aggregate(WORD ~ ., data = merge(df.lang, df.monkey, by="WORD"), FUN=length), c("LANG","OCCURRENCES")), SIZE=20000, LENGTH=i))
}
opt=theme(panel.background = element_rect(fill="gray92"),
panel.grid.minor = element_blank(),
panel.grid.major.x = element_blank(),
panel.grid.major.y = element_line(color="white", size=1.5),
plot.title = element_text(size = 35),
axis.title = element_text(size = 20, color="gray35"),
axis.text = element_text(size=16),
axis.ticks = element_blank(),
axis.line = element_line(colour = "white"))
ggplot(data=results, aes(x=LENGTH, y=OCCURRENCES/SIZE, colour=LANG))+
geom_line(size = 2)+
scale_colour_discrete(guide = FALSE) +
geom_point(aes(fill=LANG),size=10, colour="gray92",pch=21)+
scale_x_continuous("word length", labels=c("two chars", "three chars", "four chars", "five chars"))+
scale_y_continuous("probability of existence", limits=c(0, 0.4), labels = percent)+
labs(title = "What if you put a monkey in front of a typewriter?")+
opt + scale_fill_discrete(name="Dictionary", breaks=c("ESP", "ENG"), labels=c("Spanish", "English"))
(1) The English dictionary was originally compiled from public domain sources
for the amSpell spell-checker by Erik Frambach e-mail: e.h.m.frambach@eco.rug.nl
(2) The Spanish dictionary has been elaborated by Juan L. Varona, Dpto. de Matematicas y Computacion, Universidad de La Rioja, Calle Luis de Ulloa s/n, 26004 SPAIN e-mail: jvarona@siur.unirioja.es
