You can (if you will) make up the following combinations for the digits 0-9:
ch=0 t=5
sh=1 cfh=6
f=2 cph=7
p=3 ckh=8
k=4 cth=9
logic behind this scheme is:
ch # of vertical strokes=0
sh 1 upper stroke
gallows are coded like this:
loops 1 counts 0, 2 count 1
vertical strokes 1 or 2 count 2 or 4
so:
char loops strokes digit
------------------------
f 1 1 0+2=2
p 2 1 1+2=3
k 1 2 0+4=4
t 2 2 1+4=5
the surrounding c-h add 4 to the digit thus:
cfh=6,cph=7 and so on.
This is quite arbitrarly, but shows, how digits might be hidden in the text.
Cheers
CLaus
-----Ursprüngliche Nachricht-----
Von: Bruce Grant [mailto:bgrant@xxxxxxxxxxxxx]
Gesendet: Freitag, 14. Juni 2002 04:11
An: voynich@xxxxxxxxxxxxxx
Betreff: VMs: Re: VMs as Numbers
The phrases "bench bits" and "almost exactly half" make me think of something.
The gallows characters really have several dichotomous features, don't they?
That is,
- one loop vs. two loops
- two straight legs vs. a leg and a hook
- leg straddled by a bench or not
In addition, you have "bench + no hook + no gallows" and "bench + hook + no
gallows" characters. In other words, almost all the combinations of:
(no loops, one loop, two loops) x (no hook, hook) x (no bench, bench)
They could code decimal digits, though I would expect a more even distribution
if so.
Perhaps it would be a good idea to look at the joint distribution of these
features.
Bruce
Jorge Stolfi wrote:
> > [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