Biblical Hebrew Forum

["K Randolph" <kwrandolph AT gmail.com>]

Peter:

Could you do one letter by hand, showing how you came to your figures?
I don't understand your explanation, and I was unable to replicate
your results from your last letter, as far as I understood it.

This request is merely what I use to verify any formula that I
develop. I try it at least once using real numbers by hand aided by a
calculator. In this case I ask not that you solve for one letter, just
that you set up for one letter so I can see where the numbers go.
Thanks.

On 1/18/07, Peter Kirk <peter AT qaya.org> wrote:
> On 18/01/2007 19:46, K Randolph wrote:
> > ...
> > Notice that the shin has the second lowest multiple. The sin and shin
> > together have a multiple still on the low side of the average of 1.784
> > (taken from the total row).
> >
> >
> And sin has the highest multiple.

No it does not. That honor goes to zayin.

> ... You can't win that way. Also you can't
> put sin and shin together in these statistics by simple addition, so
> your added calculation is not valid - although in practice I accept that
> sin and shin taken together would fall in the middle of the range, if
> you accept sin-shin pairs as real homonyms.
I realize that. I was looking for a ballpark figure.

> > Even though I disagree with the lexicographic method, the results seem
> > to imply even stronger than defining by action that the sin and shin
> > together were originally one letter. (Defining according to action
> > gives an observed frequency closer to the predicted numbers than to
> > the "observed" frequency from your received list.)
> >
> >
> I would be interested in your statistics on the number of homonym for
> each letter defined "by action". I assume that you have these numbers as
> without them you could not observe a frequency.
I don't have the full figures. Based on a random spot check of fewer
than 100 of your homonyms, I found about a third to a little over a
half listed as homonyms according to definitions based on actions,
depending on the sample. Therefore, I extrapolate from a small sample.

> > To repeat my original observation, I noticed that sin and shin
> > together are observed to have a lower frequency of homonyms than
> > expected, especially lower than expected if they were originally two
> > phonemes. That, along with other clues, caused me to raise the
> > question, were they originally one phoneme with one letter to
> > represent that one phoneme?
> >
> >
> Well, let us see the statistics on which you based your original
> observation.
The reason you started your analysis is because I noted that I had
made an observation with no numerical analysis to back it up.

First I would have to choose a sample base. You chose verbal roots, fair 
enough.

Secondly I would have to build my database. You got yours from a
university, fair enough, good enough to make an initial analysis to
make sure we have our tools properly set up.

Then and only then could I do a numerical analysis.

> My calculations suggest that the distribution of verb roots is
> essentially random over the space of possible three letter roots, with
> no special constraint on duplicates. The implication of this is that
> there would be no difference in the frequency of homonyms between simple
> letters and those which were originally multiple letters; and thus that
> this method of counting homonyms is not helpful in deciding whether sin
> and shin were originally separate.
This is making assumptions. If consonantal phonemes were randomly
distributed, then if two were sharing the same grapheme, then the
expectation is that the grapheme would show up as a written homonym
twice as often as those graphemes not shared by two phonemes.

Well, phonemes are not randomly distributed, so we need to make
allowances for that.

> A bit more analysis....
Sorry, but I didn't understand it.

I never was very good with numbers, to the disgust of my father, who
was a math professor. My lack of understanding is most likely my
fault.

> --
> Peter Kirk
> E-mail:  peter AT qaya.org
> Blog:    http://speakertruth.blogspot.com/
> Website: http://www.qaya.org/
One question I want to know: starting with 1615 three letter verb
roots, if I pick up one, what is the probability that there is another
one in the pool that is a homonym? If one of the letters is already
known, what is the probability of finding a homonym from a pool
containing that letter? Knowing that would go a long ways towards
understanding this, I think.

Karl W. Randolph.