VMs: Re: VMs as Numbers

[Jorge Stolfi <stolfi@xxxxxxxxxxxxx>]

    > [Bruce Grant:] Speaking of encoded Roman numerals, a dead
    > giveaway ought to be the presence of seven different symbols,
    > four of which appear in multiples (I, X, C, M) and three of
    > which do not (V, L, D), and with certain forbidden diagraph
    > patterns:
    > 
    > IV,VI, IX, XI, XV =>   OK   VX => not OK
    > XL, LX, XC, CX, CL =>  OK   LC => not OK  and so on

There are indeed rules of this sort that apply to the sequence
of letters in the VMS words.  However, I haven't been able to see 
any obvious match to the patterns of standard Roman numerals.

One intriguing fact is that almost exactly half of the VMS tokens have
exactly one gallows, while the other half has none. Also, almost
exactly half of the tokens have "bench" letters (EVA ch, sh, ee); and
this "bench bit" seems to be independent of the "gallows bit". It is
therefore tempting to identify those letters with the 5's of Roman
numerals, e.g. {gallows = V, benches = L}. But then what? And why are
there 4 different gallows, and several different benches?

Perhaps the 4 gallows represent the Roman "digits" V,VI, VII, VIII,
while the benches stand for L, LX, etc.. But then what are the EVA
letters "a"/"o", and "e", which seem to be pre- and postfix modifiers
for other letters?

    > [Robert:] A quick thought. If the VMs is mostly encoded numbers,
    > then there is a fairly powerful test of this hypothesis.
    > 
    > Just as Zipf's Law predicts word frequency, so Benford's
    > Law predicts the frequencies of the initial digits of a
    > sequence of numbers.  In a nutshell, P(n) = log(n+1) - log(n)

That law may hold for "open" number sets, where the frequency
of a number decreases with its magnitude in the approrpiate way.
It is unlikely to hold for "closed" number sets, such as 
telephone numbers or train times. 

Would it hold for a numerical code? I guess that it depends on how the
numbers are assigned to the words.

All the best,

--stolfi