stuff about Roman numerals

• parsing Roman numerals, i.e. building a program that can scan a Roman numeral and decide whether it’s legal (possibly computing the integer-equivalent value at the same time), is an interesting questino with a lot of different connections. Googling “‘roman numeral’ ‘finite state machine’” returns
  • this Perl program and discussion (the last paragraph/“Postscript” is particularly funny);
  • and this great article by Brian Hayes (“the subtractive notation for Roman numerals cannot be handled by a finite-state machine … [but a push-down automaton can]). There’s a lot of interesting general computer science here.
  • PS: Hayes says “No programming language known to me allows numbers to be entered in Roman form …” Ha! in R we can do this: (str() is an R function that reports on the structure of an R object)

str(as.roman("VII"))

## Class 'roman'  int 7

• In class, one student asked if we could set the variable X=10 (for example) and use that assignment to translate values in the string. I tried to explain, not very clearly, that this was mixing up logical levels (between a symbol and a value of a string). In R I would do this as

X <- 10
r <- "XVI"
get(substr(r,1,1))

## [1] 10

I asked StackOverflow how to do this in Python. The answer:

X = 10
r = "XVI"
print(locals()[r[0]])

## 10

This question is an example of the use-mention distinction, which is played with in Lewis Carroll’s Through the Looking Glass; are we interested in the value of the symbol X, or the value of the symbol named "X"?

PPS: This feels like an example of Gelman’s God is in every leaf of every tree …